<div id="pf1" class="pf w0 h0" data-page-no="1"><div class="pc pc1 w0 h0"><img class="bi x0 y0 w1 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x2 h3 y2 ff2 fs1 fc0 sc0 ls1 ws1">CENTR<span class="blank _2"></span>O<span class="blank"> </span>UNIVERSITÁRIO<span class="blank"> </span>DE<span class="blank"> </span>TECNOLOGIA<span class="blank"> </span>DE</div><div class="t m0 x3 h3 y3 ff2 fs1 fc0 sc0 ls1">CURITIBA</div><div class="t m0 x4 h4 y4 ff3 fs1 fc0 sc0 ls1 ws2">Credenciada<span class="blank"> </span>p<span class="blank _1"> </span>ela<span class="blank"> </span>p<span class="blank _1"> </span>ortaria<span class="blank"> </span>do<span class="blank"> </span>MEC<span class="blank"> </span>n<span class="ff4 ls0">º</span>1057<span class="blank"> </span>de<span class="blank"> </span>27/12/2021,</div><div class="t m0 x5 h4 y5 ff3 fs1 fc0 sc0 ls1 ws2">publicada<span class="blank"> </span>no<span class="blank"> </span>DOU<span class="blank"> </span>em<span class="blank"> </span>28/12/2021</div><div class="t m0 x4 h4 y6 ff3 fs1 fc0 sc0 ls1 ws2">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01</div><div class="t m0 x6 h4 y7 ff3 fs1 fc0 sc0 ls1 ws2">Disciplina:<span class="blank _3"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos<span class="blank _4"> </span>NOT<span class="blank _5"></span>A:<span class="blank"> </span>Conhecimen<span class="blank _2"></span>to</div><div class="t m0 x6 h4 y8 ff3 fs1 fc0 sc0 ls1 ws2">Professor:<span class="blank _3"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div><div class="t m0 x6 h4 y9 ff3 fs1 fc0 sc0 ls1 ws3">Graduando(a):<span class="blank _6"> </span>Data:<span class="blank"> </span>/<span class="blank"> </span>/2023</div><div class="t m0 x6 h4 ya ff3 fs1 fc0 sc0 ls1 ws4">Curso:<span class="blank _3"> </span>Engenharia<span class="blank _7"> </span>Química<span class="blank _8"> </span>P<span class="blank _2"></span>erío<span class="blank"> </span>do:</div><div class="t m0 x7 h2 yb ff1 fs0 fc0 sc0 ls1 ws0">1.<span class="blank _3"> </span>Independentemen<span class="blank _2"></span>te<span class="blank"> </span>de<span class="blank"> </span>con<span class="blank _2"></span>texto,<span class="blank"> </span>p<span class="blank _1"> </span>odemos<span class="blank _9"> </span>p<span class="blank _1"> </span>ensar<span class="blank"> </span>no<span class="blank"> </span>v<span class="blank _2"></span>etor<span class="blank"> </span>como:</div><div class="t m0 x8 h2 yc ff1 fs0 fc0 sc0 ls1 ws0">A.<span class="blank _3"> </span>um<span class="blank"> </span>segmen<span class="blank _2"></span>to<span class="blank"> </span>de<span class="blank"> </span>reta<span class="blank"> </span>orien<span class="blank _2"></span>tado.</div><div class="t m0 x8 h2 yd ff1 fs0 fc0 sc0 ls1 ws0">B.<span class="blank _3"> </span>um<span class="blank"> </span>segmen<span class="blank _2"></span>to<span class="blank"> </span>de<span class="blank"> </span>reta<span class="blank"> </span>qualquer.</div><div class="t m0 x9 h5 ye ff5 fs0 fc1 sc0 ls1 ws5">C.<span class="blank _3"> </span>uma<span class="blank"> </span>en<span class="blank _2"></span>tidade<span class="blank"> </span>de<span class="blank"> </span>transmite<span class="blank"> </span>informação.</div><div class="t m0 x8 h2 yf ff1 fs0 fc0 sc0 ls1 ws0">D.<span class="blank _3"> </span>animais<span class="blank"> </span>que<span class="blank"> </span>transmitem<span class="blank"> </span>doenças.</div><div class="t m0 x8 h2 y10 ff1 fs0 fc0 sc0 ls1 ws0">E.<span class="blank _3"> </span>form<span class="blank _2"></span>ulários<span class="blank"> </span>com<span class="blank"> </span>informações<span class="blank"> </span>de<span class="blank"> </span>alguém.</div><div class="t m0 x7 h2 y11 ff1 fs0 fc0 sc0 ls1 ws0">2.<span class="blank _3"> </span>Os<span class="blank"> </span>eixos<span class="blank"> </span>do<span class="blank"> </span>plano<span class="blank"> </span>cartesiano<span class="blank"> </span>e<span class="blank"> </span>do<span class="blank"> </span>espaço<span class="blank"> </span>euclidiano<span class="blank"> </span>represen<span class="blank _2"></span>tam<span class="blank"> </span>o<span class="blank"> </span>conjun<span class="blank _2"></span>to<span class="blank"> </span>dos<span class="blank"> </span>n<span class="blank _2"></span>úmeros:</div><div class="t m0 xa h2 y12 ff1 fs0 fc0 sc0 ls1 ws6">A.<span class="blank"> </span>complexos.<span class="blank _a"> </span><span class="ff5 fc1 ws7">B.<span class="blank"> </span>reais.<span class="blank _b"> </span></span>C.<span class="blank"> </span>in<span class="blank _2"></span>teiros.<span class="blank _c"> </span>D.<span class="blank"> </span>naturais.<span class="blank _c"> </span>E.<span class="blank"> </span>racionais.</div><div class="t m0 x7 h2 y13 ff1 fs0 fc0 sc0 ls1 ws8">3.<span class="blank _3"> </span>Em<span class="blank _2"></span>bora<span class="blank"> </span>muitas<span class="blank"> </span>pessoas<span class="blank"> </span>chamem<span class="blank"> </span>os<span class="blank"> </span>eixos<span class="blank"> </span>pelos<span class="blank"> </span>ap<span class="blank _1"> </span>elidos<span class="blank"> </span>\u201ceixo<span class="blank"> </span>x\u201d,<span class="blank"> </span>\u201ceixo<span class="blank"> </span>y\u201d<span class="blank _d"> </span>e<span class="blank"> </span>\u201ceixo<span class="blank"> </span>z\u201d,<span class="blank"> </span>o<span class="blank"> </span>nome<span class="blank"> </span>correto<span class="blank"> </span>deles,<span class="blank"> </span>resp<span class="blank _1"> </span>ec-</div><div class="t m0 xa h2 y14 ff1 fs0 fc0 sc0 ls1 ws0">tiv<span class="blank _2"></span>amen<span class="blank _2"></span>te,<span class="blank"> </span>são:</div><div class="t m0 x9 h5 y15 ff5 fs0 fc1 sc0 ls1 ws5">A.<span class="blank _3"> </span>abscissa,<span class="blank"> </span>ordenada<span class="blank"> </span>e<span class="blank"> </span>cota.</div><div class="t m0 x8 h2 y16 ff1 fs0 fc0 sc0 ls1 ws0">B.<span class="blank _3"> </span>ordenada,<span class="blank"> </span>abscissa<span class="blank"> </span>e<span class="blank"> </span>cota.</div><div class="t m0 x8 h2 y17 ff1 fs0 fc0 sc0 ls1 ws0">C.<span class="blank _3"> </span>abscissa,<span class="blank"> </span>cota<span class="blank"> </span>e<span class="blank"> </span>ordenada.</div><div class="t m0 x8 h2 y18 ff1 fs0 fc0 sc0 ls1 ws0">D.<span class="blank _3"> </span>cota,<span class="blank"> </span>abscissa<span class="blank"> </span>e<span class="blank"> </span>ordenada.</div><div class="t m0 x8 h2 y19 ff1 fs0 fc0 sc0 ls1 ws0">E.<span class="blank _3"> </span>ordenada,<span class="blank"> </span>cota<span class="blank"> </span>e<span class="blank"> </span>abscissa.</div><div class="t m0 x7 h2 y1a ff1 fs0 fc0 sc0 ls1 ws0">4.<span class="blank _3"> </span>Em<span class="blank"> </span>nossa<span class="blank"> </span>disciplina,<span class="blank"> </span>neste<span class="blank"> </span>primeiro<span class="blank"> </span>momen<span class="blank _2"></span>to,<span class="blank"> </span>as<span class="blank"> </span>informações<span class="blank"> </span>que<span class="blank"> </span>os<span class="blank"> </span>vetores<span class="blank"> </span>irão<span class="blank"> </span>transmitir<span class="blank"> </span>são:</div><div class="t m0 x8 h2 y1b ff1 fs0 fc0 sc0 ls1 ws9">A.<span class="blank _3"> </span>deslocamentos.</div><div class="t m0 x8 h2 y1c ff1 fs0 fc0 sc0 ls1 ws0">B.<span class="blank _3"> </span>in<span class="blank _2"></span>tensidade<span class="blank"> </span>de<span class="blank"> </span>forças.</div><div class="t m0 x8 h2 y1d ff1 fs0 fc0 sc0 ls1 ws0">C.<span class="blank _3"> </span>temperatura,<span class="blank"> </span>pressão<span class="blank"> </span>e<span class="blank"> </span>volume.</div><div class="t m0 x8 h2 y1e ff1 fs0 fc0 sc0 ls1 ws0">D.<span class="blank _3"> </span>largura,<span class="blank"> </span>comprimen<span class="blank _2"></span>to<span class="blank"> </span>e<span class="blank"> </span>profundidade.</div><div class="t m0 x9 h5 y1f ff5 fs0 fc1 sc0 ls1 ws5">E.<span class="blank _3"> </span>direção,<span class="blank"> </span>sen<span class="blank _2"></span>tido<span class="blank"> </span>e<span class="blank"> </span>in<span class="blank _2"></span>tensidade.</div><div class="t m0 x7 h2 y20 ff1 fs0 fc0 sc0 ls1 ws0">5.<span class="blank _3"> </span>Sobre<span class="blank"> </span>os<span class="blank"> </span>v<span class="blank _2"></span>etores,<span class="blank"> </span>está<span class="blank"> </span>incorreto<span class="blank"> </span>a<span class="blank"> </span>seguin<span class="blank _2"></span>te<span class="blank"> </span>informação:</div><div class="t m0 x8 h2 y21 ff1 fs0 fc0 sc0 ls1 wsa">A.<span class="blank _3"> </span>A<span class="blank"> </span>in<span class="blank _2"></span>tensidade,<span class="blank"> </span>magnitude<span class="blank"> </span>ou<span class="blank"> </span>mó<span class="blank _1"> </span>dulo<span class="blank"> </span>do<span class="blank"> </span>vetor<span class="blank"> </span>é<span class="blank"> </span>represen<span class="blank _2"></span>tado<span class="blank"> </span>geometricamen<span class="blank _2"></span>te<span class="blank"> </span>p<span class="blank _1"> </span>elo<span class="blank"> </span>tamanho<span class="blank"> </span>do<span class="blank"> </span>segmen<span class="blank _2"></span>to</div><div class="t m0 xb h2 y22 ff1 fs0 fc0 sc0 ls1 ws0">de<span class="blank"> </span>reta<span class="blank"> </span>orien<span class="blank _2"></span>tado.</div><div class="t m0 x8 h2 y23 ff1 fs0 fc0 sc0 ls1 ws0">B.<span class="blank _3"> </span>A<span class="blank"> </span>direção<span class="blank"> </span>sempre<span class="blank"> </span>apresen<span class="blank _2"></span>ta<span class="blank"> </span>dois<span class="blank"> </span>sen<span class="blank _2"></span>tidos.</div><div class="t m0 x8 h2 y24 ff1 fs0 fc0 sc0 ls1 ws0">C.<span class="blank _3"> </span>Uma<span class="blank"> </span>forma<span class="blank"> </span>de<span class="blank"> </span>lem<span class="blank _2"></span>brar<span class="blank"> </span>a<span class="blank"> </span>diferença<span class="blank"> </span>en<span class="blank _2"></span>tre<span class="blank"> </span>sen<span class="blank _2"></span>tido<span class="blank"> </span>e<span class="blank"> </span>direção<span class="blank"> </span>é<span class="blank"> </span>lembrar:<span class="blank _d"> </span>SEn<span class="blank _2"></span>tido<span class="blank"> </span>e<span class="blank"> </span>SEta.</div><div class="t m0 x9 h5 y25 ff5 fs0 fc1 sc0 ls1 ws5">D.<span class="blank _3"> </span>Direção<span class="blank"> </span>e<span class="blank"> </span>sen<span class="blank _2"></span>tido<span class="blank"> </span>são<span class="blank"> </span>sinônimos.</div><div class="t m0 x8 h2 y26 ff1 fs0 fc0 sc0 ls1 ws0">E.<span class="blank _3"> </span>A<span class="blank"> </span>direção<span class="blank"> </span>po<span class="blank _1"> </span>de<span class="blank"> </span>ser<span class="blank"> </span>p<span class="blank _1"> </span>ensada<span class="blank"> </span>como<span class="blank"> </span>um<span class="blank"> </span>ângulo<span class="blank"> </span>em<span class="blank"> </span>relação<span class="blank"> </span>a<span class="blank"> </span>um<span class="blank"> </span>determinado<span class="blank"> </span>referencial.</div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>1<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf2" class="pf w0 h0" data-page-no="2"><div class="pc pc2 w0 h0"><img class="bi x0 y0 w2 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x7 h2 y28 ff1 fs0 fc0 sc0 ls1 ws8">6.<span class="blank _3"> </span>Localize<span class="blank"> </span>os<span class="blank"> </span>seguintes<span class="blank"> </span>pontos<span class="blank"> </span>no<span class="blank"> </span>plano<span class="blank"> </span>cartesiano:<span class="blank _d"> </span><span class="ff6 ls2">A</span><span class="ff7 wsc">=<span class="blank"> </span>(5<span class="ff6 ls3">,</span><span class="wsd">4)</span></span><span class="ls4">;<span class="ff6 ls5">B</span></span><span class="ff7 wsc">=<span class="blank"> </span>(0<span class="ff6 ls3">,</span><span class="wsd">3)</span></span><span class="ls6">;<span class="ff6 ls7">C</span></span><span class="ff7 wsc">=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span><span class="wsd">1<span class="ff6 ls3">,<span class="ff8 ls8">\u2212</span></span>5)</span></span><span class="ls4">;<span class="ff6 ls9">D</span></span><span class="ff7 wse">=<span class="blank"> </span>(<span class="ff8 wsf">\u2212</span><span class="lsa">4<span class="ff6 lsb">,</span></span><span class="wsd">0)</span></span><span class="ls4">;<span class="ff6 lsc">E</span></span><span class="ff7 wse">=<span class="blank"> </span>(3<span class="ff6 ls3">,<span class="ff8 ls8">\u2212</span></span><span class="wsd">3)</span></span>;</div><div class="t m0 xa h2 y29 ff6 fs0 fc0 sc0 lsd">F<span class="ff7 ls1 wse">=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span><span class="wsd">2</span></span><span class="ls3">,<span class="ff7 ls1 wsd">1)<span class="ff1 lse">;</span></span><span class="lsf">G<span class="ff7 ls1 wse">=<span class="blank"> </span>(1</span></span>,<span class="ff7 ls1 wsd">0)<span class="ff1 lse">;</span></span><span class="ls10">H<span class="ff7 ls1 wse">=<span class="blank"> </span>(0</span></span>,<span class="ff8 ls8">\u2212<span class="ff7 ls1 wsd">2)<span class="ff1">.</span></span></span></span></div><div class="t m0 xc h6 y2a ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls12">5</span><span class="ls1 ws10">\u2212<span class="ff7 ls12">4</span></span>\u2212<span class="ff7 ls12">3</span>\u2212<span class="ff7 ls12">2</span>\u2212<span class="ff7 ls1 ws11">1<span class="blank _10"> </span>1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4<span class="blank"> </span>5</span></div><div class="t m0 xd h6 y2b ff8 fs2 fc0 sc0 ls1 ws10">\u2212<span class="ff7">5</span></div><div class="t m0 xd h6 y2c ff8 fs2 fc0 sc0 ls1 ws10">\u2212<span class="ff7">4</span></div><div class="t m0 xd h6 y2d ff8 fs2 fc0 sc0 ls1 ws10">\u2212<span class="ff7">3</span></div><div class="t m0 xd h6 y2e ff8 fs2 fc0 sc0 ls1 ws10">\u2212<span class="ff7">2</span></div><div class="t m0 xd h6 y2f ff8 fs2 fc0 sc0 ls1 ws10">\u2212<span class="ff7">1</span></div><div class="t m0 xe h6 y30 ff7 fs2 fc0 sc0 ls1">1</div><div class="t m0 xe h6 y31 ff7 fs2 fc0 sc0 ls1">2</div><div class="t m0 xe h6 y32 ff7 fs2 fc0 sc0 ls1">3</div><div class="t m0 xe h6 y33 ff7 fs2 fc0 sc0 ls1">4</div><div class="t m0 xe h6 y34 ff7 fs2 fc0 sc0 ls1">5</div><div class="t m0 xf h7 y35 ff6 fs2 fc0 sc0 ls1">x</div><div class="t m0 x10 h7 y36 ff6 fs2 fc0 sc0 ls1">y</div><div class="t m0 x11 h8 y37 ff8 fs0 fc1 sc0 ls8">\u2212<span class="ff7 ls13">5</span>\u2212<span class="ff7 ls14">4</span>\u2212<span class="ff7 ls14">3</span><span class="ls1 wsf v0">\u2212<span class="ff7 ls14">2</span><span class="ls8">\u2212</span><span class="ff7 ws12">1<span class="blank _11"> </span>1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4<span class="blank"> </span>5</span></span></div><div class="t m0 xe h9 y38 ff8 fs0 fc1 sc0 ls8">\u2212<span class="ff7 ls1">5</span></div><div class="t m0 xe h9 y39 ff8 fs0 fc1 sc0 ls8">\u2212<span class="ff7 ls1">4</span></div><div class="t m0 xe h9 y3a ff8 fs0 fc1 sc0 ls8">\u2212<span class="ff7 ls1">3</span></div><div class="t m0 xe h9 y3b ff8 fs0 fc1 sc0 ls8">\u2212<span class="ff7 ls1">2</span></div><div class="t m0 xe h9 y3c ff8 fs0 fc1 sc0 ls8">\u2212<span class="ff7 ls1">1</span></div><div class="t m0 x12 h9 y3d ff7 fs0 fc1 sc0 ls1">1</div><div class="t m0 x12 h9 y3e ff7 fs0 fc1 sc0 ls1">2</div><div class="t m0 x12 h9 y3f ff7 fs0 fc1 sc0 ls1">3</div><div class="t m0 x12 h9 y40 ff7 fs0 fc1 sc0 ls1">4</div><div class="t m0 x12 h9 y41 ff7 fs0 fc1 sc0 ls1">5</div><div class="c x13 y42 w3 ha"><div class="t m0 x14 hb y43 ff6 fs0 fc2 sc0 ls1">A</div><div class="t m0 x15 hb y44 ff6 fs0 fc2 sc0 ls1">B</div><div class="t m0 x16 hb y45 ff6 fs0 fc2 sc0 ls1">C</div><div class="t m0 x17 hb y46 ff6 fs0 fc2 sc0 ls1">D</div><div class="t m0 x18 hb y47 ff6 fs0 fc2 sc0 ls1">E</div><div class="t m0 x19 hb y48 ff6 fs0 fc2 sc0 ls1">F</div><div class="t m0 x1a hb y46 ff6 fs0 fc2 sc0 ls1">G</div><div class="t m0 x15 hb y49 ff6 fs0 fc2 sc0 ls1">H</div></div><div class="t m0 x1b hb y4a ff6 fs0 fc1 sc0 ls1">x</div><div class="t m0 x1c hb y4b ff6 fs0 fc1 sc0 ls1">y</div><div class="t m0 x7 h2 y4c ff1 fs0 fc0 sc0 ls1 ws0">7.<span class="blank _3"> </span>Utilizando<span class="blank"> </span>as<span class="blank"> </span>coordenadas<span class="blank"> </span>dos<span class="blank"> </span>p<span class="blank _1"> </span>ontos<span class="blank"> </span>do<span class="blank"> </span>exercício<span class="blank"> </span>an<span class="blank _2"></span>terior,<span class="blank"> </span>determine<span class="blank"> </span>as<span class="blank"> </span>componentes<span class="blank"> </span>dos<span class="blank"> </span>seguin<span class="blank _2"></span>tes<span class="blank"> </span>v<span class="blank _2"></span>etores:</div><div class="t m0 x1d hc y4d ff1 fs0 fc0 sc0 ls1 ws13">(a)<span class="blank"> </span><span class="ff6 ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _13"></span>\u2212<span class="blank _13"></span>\u2192</span></span></div><div class="t m0 x1e hc y4d ff6 fs0 fc0 sc0 ls1 ws15">D<span class="blank"> </span>F<span class="blank _14"> </span><span class="ff1 ws16">(b)<span class="blank"> </span></span><span class="ws17">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _15"></span>\u2212<span class="blank _15"></span>\u2192</span></span></div><div class="t m0 x1f hc y4d ff6 fs0 fc0 sc0 ls1 ws18">H<span class="blank"> </span>B<span class="blank _14"> </span><span class="ff1 ws19">(c)<span class="blank"> </span></span><span class="ws1a">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _12"></span>\u2212<span class="blank _12"></span>\u2192</span></span></div><div class="t m0 x20 hd y4d ff6 fs0 fc0 sc0 ls1 ws1b">C<span class="blank"> </span>E<span class="blank _17"> </span><span class="ff1 ws1c">(d)<span class="blank"> </span></span><span class="v2">\ue67e</span></div><div class="t m0 x21 hc y4d ff6 fs0 fc0 sc0 ls16">t<span class="ff7 ls15">=<span class="ff8 ls1 wsf v1">\u2212<span class="blank _12"></span>\u2212<span class="blank _12"></span>\u2192</span></span></div><div class="t m0 x22 hb y4d ff6 fs0 fc0 sc0 ls1 ws1d">E<span class="blank"> </span>C</div><div class="t m0 x23 he y4e ff1 fs0 fc1 sc0 ls1 ws13">(a)<span class="blank"> </span><span class="ff6 ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _13"></span>\u2212<span class="blank _13"></span>\u2192</span></span></div><div class="t m0 x24 h9 y4e ff6 fs0 fc1 sc0 ls1 ws15">D<span class="blank"> </span>F<span class="blank _7"> </span><span class="ff7 ls15">=</span><span class="ls17">F<span class="ff8 ls18">\u2212</span><span class="ls19">D</span></span><span class="ff7 wse">=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span><span class="wsd">2</span></span><span class="ls3">,</span><span class="ff7 ws1e">1)<span class="blank"> </span><span class="ff8 ls1a">\u2212</span><span class="ls1b">(</span><span class="ff8 wsf">\u2212</span><span class="lsa">4</span></span><span class="ls3">,</span><span class="ff7 ws1f">0)<span class="blank"> </span>=<span class="blank"> </span>(2</span><span class="ls3">,</span><span class="ff7">1)</span></div><div class="t m0 x23 hc y4f ff1 fs0 fc1 sc0 ls1 ws20">(b)<span class="blank"> </span><span class="ff6 ws21">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff7 ls1c">=</span><span class="ff8 wsf v1">\u2212<span class="blank _12"></span>\u2212<span class="blank _12"></span>\u2192</span></span></div><div class="t m0 x24 h9 y4f ff6 fs0 fc1 sc0 ls1 ws22">F<span class="blank"> </span>B<span class="blank _18"> </span><span class="ff7 ls15">=</span><span class="ls1d">B<span class="ff8 ls18">\u2212</span><span class="ls1e">F</span></span><span class="ff7 wse">=<span class="blank"> </span>(0</span><span class="ls3">,</span><span class="ff7 ws1e">3)<span class="blank"> </span><span class="ff8 ls1a">\u2212</span><span class="ls1b">(</span><span class="ff8 wsf">\u2212</span><span class="lsa">2</span></span><span class="lsb">,</span><span class="ff7 wse">1)<span class="blank"> </span>=<span class="blank"> </span>(2</span><span class="ls3">,</span><span class="ff7">2)</span></div><div class="t m0 x1 h2 y50 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>2<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf3" class="pf w0 h0" data-page-no="3"><div class="pc pc3 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w2 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg3.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x23 he y51 ff1 fs0 fc1 sc0 ls1 ws23">(c)<span class="blank"> </span><span class="ff6 ws24">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _12"></span>\u2212<span class="blank _12"></span>\u2192</span></span></div><div class="t m0 x25 h9 y51 ff6 fs0 fc1 sc0 ls1 ws1b">C<span class="blank"> </span>E<span class="blank _18"> </span><span class="ff7 ls15">=</span><span class="ls1f">E<span class="ff8 ls1a">\u2212</span><span class="ls20">C</span></span><span class="ff7 wse">=<span class="blank"> </span>(3</span><span class="lsb">,<span class="ff8 ls8">\u2212</span></span><span class="ff7 ws1e">3)<span class="blank"> </span><span class="ff8 ls1a">\u2212</span><span class="ls1b">(<span class="ff8 ls8">\u2212</span></span><span class="wsd">1</span></span><span class="ls3">,</span><span class="ff8 wsf">\u2212<span class="ff7 wse">5)<span class="blank"> </span>=<span class="blank"> </span>(4</span></span><span class="ls3">,</span><span class="ff7">2)</span></div><div class="t m0 x23 hf y52 ff1 fs0 fc1 sc0 ls1 ws1c">(d)<span class="blank"> </span><span class="ff6 v2">\ue67e</span></div><div class="t m0 x15 he y52 ff6 fs0 fc1 sc0 ls16">t<span class="ff7 ls15">=<span class="ff8 ls1 wsf v1">\u2212<span class="blank _12"></span>\u2212<span class="blank _12"></span>\u2192</span></span></div><div class="t m0 x26 h9 y52 ff6 fs0 fc1 sc0 ls1 ws1d">E<span class="blank"> </span>C<span class="blank _18"> </span><span class="ff7 ls15">=</span><span class="ls21">C<span class="ff8 ls18">\u2212</span><span class="ls22">E</span></span><span class="ff7 wse">=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span><span class="lsa">1</span></span><span class="lsb">,<span class="ff8 ls8">\u2212</span></span><span class="ff7 ws1e">5)<span class="blank"> </span><span class="ff8 ls1a">\u2212</span><span class="wsd">(3</span></span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7 ws1f">3)<span class="blank"> </span>=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span><span class="wsd">4</span></span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7">2)</span></div><div class="t m0 x7 h2 y53 ff1 fs0 fc0 sc0 ls1 ws25">8.<span class="blank"> </span>Lo<span class="blank _1"> </span>calize<span class="blank"> </span>os<span class="blank"> </span>seguintes<span class="blank"> </span>pontos<span class="blank"> </span>no<span class="blank"> </span>espaço<span class="blank"> </span>euclidiano:<span class="blank _19"> </span><span class="ff6 ls23">A</span><span class="ff7 ws26">=<span class="blank"> </span>(1<span class="ff6 ls3">,</span><span class="wsd">2<span class="ff6 ls3">,</span>2)</span></span><span class="ls24">,<span class="ff6 ls25">B</span></span><span class="ff7 ws26">=<span class="blank"> </span>(4<span class="ff6 ls3">,</span><span class="wsd">3<span class="ff6 ls3">,</span>0)</span></span><span class="ls24">,<span class="ff6 ls26">C</span></span><span class="ff7 ws26">=<span class="blank"> </span>(3<span class="ff6 ls3">,</span><span class="wsd">0<span class="ff6 ls3">,</span>0)</span></span><span class="ls27">,<span class="ff6 ls28">D</span></span><span class="ff7 ws26">=<span class="blank"> </span>(4<span class="ff6 ls3">,</span><span class="wsd">0<span class="ff6 ls3">,</span>5)</span></span>,</div><div class="t m0 xa h2 y54 ff6 fs0 fc0 sc0 ls22">E<span class="ff7 ls1 wse">=<span class="blank"> </span>(0</span><span class="ls3">,<span class="ff7 ls1 wsd">0</span>,<span class="ff7 ls1 wsd">3)<span class="ff1 ls29">,</span></span><span class="lsd">F<span class="ff7 ls1 wse">=<span class="blank"> </span>(2</span></span>,<span class="ff7 ls1 wsd">7</span>,<span class="ff7 ls1 wsd">3)<span class="ff1 lse">,</span></span><span class="ls2a">G<span class="ff7 ls1 wse">=<span class="blank"> </span>(0</span></span>,<span class="ff7 lsa">7</span><span class="lsb">,<span class="ff7 ls1 wsd">0)<span class="ff1 lse">,</span></span><span class="ls10">H<span class="ff7 ls1 wse">=<span class="blank"> </span>(3</span></span></span>,<span class="ff7 ls1 wsd">6</span>,<span class="ff7 ls1 ws27">4)<span class="blank"> </span><span class="ff1 ls2b">e</span></span><span class="ls2c">I<span class="ff7 ls1 wse">=<span class="blank"> </span>(5</span></span>,<span class="ff7 ls1 wsd">8</span>,<span class="ff7 ls1 wsd">1)<span class="ff1">.</span></span></span></div><div class="t m0 x27 hb y55 ff6 fs0 fc0 sc0 ls1">z</div><div class="t m0 x28 hb y56 ff6 fs0 fc0 sc0 ls1">y</div><div class="t m0 x1e hb y57 ff6 fs0 fc0 sc0 ls1">x</div><div class="t m0 x29 h2 y58 ff1 fs0 fc0 sc0 ls1 ws28">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4<span class="blank"> </span>5<span class="blank"> </span>6<span class="blank"> </span>7<span class="blank"> </span>8</div><div class="t m0 x27 h2 y59 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x27 h2 y5a ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x27 h2 y5b ff1 fs0 fc0 sc0 ls1">3</div><div class="t m0 x27 h2 y5c ff1 fs0 fc0 sc0 ls1">4</div><div class="t m0 x27 h2 y5d ff1 fs0 fc0 sc0 ls1">5</div><div class="t m0 x2a h2 y58 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x2b h2 y5e ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x2c h2 y5f ff1 fs0 fc0 sc0 ls1">3</div><div class="t m0 x2d h2 y60 ff1 fs0 fc0 sc0 ls1">4</div><div class="t m0 x2e h2 y61 ff1 fs0 fc0 sc0 ls1">5</div><div class="t m0 x2f hb y62 ff6 fs0 fc1 sc0 ls1">z</div><div class="t m0 x30 hb y63 ff6 fs0 fc1 sc0 ls1">y</div><div class="t m0 x8 hb y64 ff6 fs0 fc1 sc0 ls1">x</div><div class="t m0 x31 h2 y65 ff1 fs0 fc1 sc0 ls1 ws29">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4<span class="blank"> </span>5<span class="blank"> </span>6<span class="blank"> </span>7<span class="blank"> </span>8</div><div class="t m0 x2f h2 y66 ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x2f h2 y67 ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x2f h2 y68 ff1 fs0 fc1 sc0 ls1">3</div><div class="t m0 x2f h2 y69 ff1 fs0 fc1 sc0 ls1">4</div><div class="t m0 x2f h2 y6a ff1 fs0 fc1 sc0 ls1">5</div><div class="t m0 x32 h2 y65 ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x11 h2 y6b ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x33 h2 y6c ff1 fs0 fc1 sc0 ls1">3</div><div class="t m0 x34 h2 y6d ff1 fs0 fc1 sc0 ls1">4</div><div class="t m0 x35 h2 y6e ff1 fs0 fc1 sc0 ls1">5</div><div class="t m0 x36 hb y6f ff6 fs0 fc2 sc0 ls1">A</div><div class="t m0 x37 hb y70 ff6 fs0 fc1 sc0 ls1">B</div><div class="t m0 x38 hb y71 ff6 fs0 fc3 sc0 ls1">C</div><div class="t m0 x39 hb y72 ff6 fs0 fc4 sc0 ls2d">D<span class="fc5 ls1">E</span></div><div class="t m0 x3a hb y73 ff6 fs0 fc6 sc0 ls1">F</div><div class="t m0 x3b hb y74 ff6 fs0 fc7 sc0 ls1">G</div><div class="t m0 x3c hb y75 ff6 fs0 fc8 sc0 ls1">H</div><div class="t m0 x3d hb y76 ff6 fs0 fc9 sc0 ls1">I</div><div class="t m0 x1 h2 y50 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>3<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf4" class="pf w0 h0" data-page-no="4"><div class="pc pc4 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w2 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg4.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x7 h2 y28 ff1 fs0 fc0 sc0 ls1 ws0">9.<span class="blank _3"> </span>Utilizando<span class="blank"> </span>as<span class="blank"> </span>coordenadas<span class="blank"> </span>dos<span class="blank"> </span>p<span class="blank _1"> </span>ontos<span class="blank"> </span>do<span class="blank"> </span>exercício<span class="blank"> </span>an<span class="blank _2"></span>terior,<span class="blank"> </span>determine<span class="blank"> </span>as<span class="blank"> </span>componentes<span class="blank"> </span>dos<span class="blank"> </span>seguin<span class="blank _2"></span>tes<span class="blank"> </span>v<span class="blank _2"></span>etores:</div><div class="t m0 x1d hc y77 ff1 fs0 fc0 sc0 ls1 ws13">(a)<span class="blank"> </span><span class="ff6 ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _12"></span>\u2192</span></span></div><div class="t m0 x1e hc y77 ff6 fs0 fc0 sc0 ls1 ws2a">GI<span class="blank"> </span><span class="ff1 ws20">(b)<span class="blank"> </span></span><span class="ws17">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _1a"></span>\u2192</span></span></div><div class="t m0 x1f hc y77 ff6 fs0 fc0 sc0 ls1 ws2b">AC<span class="blank"> </span><span class="ff1 ws19">(c)<span class="blank"> </span></span><span class="ws24">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="ff7 ls1c">=</span><span class="ff8 wsf v1">\u2212<span class="blank _13"></span>\u2212<span class="blank _15"></span>\u2192</span></span></div><div class="t m0 x20 hd y77 ff6 fs0 fc0 sc0 ls1 ws15">D<span class="blank"> </span>B<span class="blank _1b"> </span><span class="ff1 ws2c">(d)<span class="blank"> </span></span><span class="v2">\ue67e</span></div><div class="t m0 x21 hc y77 ff6 fs0 fc0 sc0 ls16">t<span class="ff7 ls15">=<span class="ff8 ls1 wsf v1">\u2212<span class="blank _1a"></span>\u2192</span></span></div><div class="t m0 x22 hb y77 ff6 fs0 fc0 sc0 ls1 ws22">F<span class="blank"> </span>A</div><div class="t m0 x23 hc y78 ff1 fs0 fc1 sc0 ls1 ws13">(a)<span class="blank"> </span><span class="ff6 ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _12"></span>\u2192</span></span></div><div class="t m0 x24 h9 y78 ff6 fs0 fc1 sc0 ls1 ws2d">GI<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ls2e">I<span class="ff8 ls1a">\u2212</span><span class="ls2a">G</span></span><span class="ff7 wse">=<span class="blank"> </span>(5</span><span class="lsb">,<span class="ff7 lsa">8</span><span class="ls3">,</span></span><span class="ff7 ws2e">1)<span class="blank"> </span><span class="ff8 ls18">\u2212</span><span class="wsd">(0</span></span><span class="ls3">,<span class="ff7 lsa">7</span><span class="lsb">,</span></span><span class="ff7 wse">0)<span class="blank"> </span>=<span class="blank"> </span>(5</span><span class="ls3">,</span><span class="ff7 wsd">7</span><span class="ls3">,</span><span class="ff7">1)</span></div><div class="t m0 x23 hc y79 ff1 fs0 fc1 sc0 ls1 ws20">(b)<span class="blank"> </span><span class="ff6 ws21">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _1a"></span>\u2192</span></span></div><div class="t m0 x24 h9 y79 ff6 fs0 fc1 sc0 ls1 ws2f">AC<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ls21">C<span class="ff8 ls18">\u2212</span><span class="ls2f">A</span></span><span class="ff7 wse">=<span class="blank"> </span>(3</span><span class="lsb">,<span class="ff7 lsa">0</span><span class="ls3">,</span></span><span class="ff7 ws2e">0)<span class="blank"> </span><span class="ff8 ls18">\u2212</span><span class="wsd">(1</span></span><span class="lsb">,<span class="ff7 lsa">2</span>,</span><span class="ff7 wse">2)<span class="blank"> </span>=<span class="blank"> </span>(2</span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7 wsd">2</span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7">2)</span></div><div class="t m0 x23 he y7a ff1 fs0 fc1 sc0 ls1 ws19">(c)<span class="blank"> </span><span class="ff6 ws24">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="ff7 ls15">=</span><span class="ff8 wsf v1">\u2212<span class="blank _13"></span>\u2212<span class="blank _15"></span>\u2192</span></span></div><div class="t m0 x25 h9 y7a ff6 fs0 fc1 sc0 ls1 ws15">D<span class="blank"> </span>B<span class="blank _18"> </span><span class="ff7 ls15">=</span><span class="ls30">B<span class="ff8 ls1a">\u2212</span><span class="ls31">D</span></span><span class="ff7 wse">=<span class="blank"> </span>(4</span><span class="lsb">,<span class="ff7 lsa">3</span><span class="ls3">,</span></span><span class="ff7 ws2e">0)<span class="blank"> </span><span class="ff8 ls18">\u2212</span><span class="wsd">(4</span></span><span class="ls3">,<span class="ff7 lsa">0</span><span class="lsb">,</span></span><span class="ff7 wse">5)<span class="blank"> </span>=<span class="blank"> </span>(0</span><span class="ls3">,</span><span class="ff7 wsd">3</span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7">5)</span></div><div class="t m0 x23 hd y7b ff1 fs0 fc1 sc0 ls1 ws1c">(d)<span class="blank"> </span><span class="ff6 v2">\ue67e</span></div><div class="t m0 x15 he y7b ff6 fs0 fc1 sc0 ls16">t<span class="ff7 ls15">=<span class="ff8 ls1 wsf v1">\u2212<span class="blank _1a"></span>\u2192</span></span></div><div class="t m0 x26 h9 y7b ff6 fs0 fc1 sc0 ls1 ws22">F<span class="blank"> </span>A<span class="blank _1c"> </span><span class="ff7 ls15">=</span><span class="ls32">A<span class="ff8 ls18">\u2212</span><span class="ls1e">F</span></span><span class="ff7 wse">=<span class="blank"> </span>(1</span><span class="ls3">,</span><span class="ff7 wsd">2</span><span class="ls3">,</span><span class="ff7 ws1e">2)<span class="blank"> </span><span class="ff8 ls1a">\u2212</span><span class="wsd">(2</span></span><span class="ls3">,</span><span class="ff7 wsd">7</span><span class="ls3">,</span><span class="ff7 wse">3)<span class="blank"> </span>=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span><span class="wsd">1</span></span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7 wsd">5</span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7">1)</span></div><div class="t m0 x1 h2 y7c ff1 fs0 fc0 sc0 ls1 ws30">10.<span class="blank _3"> </span>Represen<span class="blank _2"></span>te<span class="blank"> </span>geometricamen<span class="blank _2"></span>te<span class="blank"> </span>cada<span class="blank"> </span>v<span class="blank _2"></span>etor<span class="blank"> </span>a<span class="blank"> </span>seguir<span class="blank"> </span>considerando<span class="blank"> </span>como<span class="blank"> </span>origem<span class="blank"> </span>cada<span class="blank"> </span>um<span class="blank"> </span>dos<span class="blank"> </span>seguintes<span class="blank"> </span>pontos:<span class="blank _1d"> </span><span class="ff6 ls33">O</span><span class="ff7">=</span></div><div class="t m0 xa h2 y7d ff7 fs0 fc0 sc0 ls1 wsd">(0<span class="ff6 ls3">,</span>0)<span class="ff1 lse">,<span class="ff6 ls34">P</span></span><span class="wse">=<span class="blank"> </span>(4<span class="ff6 ls3">,</span></span>3)<span class="ff1 ls29">,<span class="ff6 ls35">Q</span></span><span class="wse">=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span></span>4<span class="ff6 ls3">,<span class="ff8 ls8">\u2212</span></span>2)<span class="ff1 ls29">,<span class="ff6 ls36">R</span></span><span class="wse">=<span class="blank"> </span>(<span class="ff8 wsf">\u2212</span><span class="lsa">5<span class="ff6 ls3">,</span></span><span class="ws31">2)<span class="blank"> </span><span class="ff1 ls2b">e<span class="ff6 ls37">S</span></span></span>=<span class="blank"> </span>(3<span class="ff6 lsb">,<span class="ff8 ls8">\u2212</span></span></span>3)<span class="ff1">:</span></div><div class="t m0 x2 hd y7e ff6 fs0 fc0 sc0 ls1 ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(3</span><span class="ls3">,</span><span class="ff7 wsd">2)</span><span class="ws32">,<span class="blank"> </span>\ue67e<span class="blank _13"></span>v<span class="blank _18"> </span><span class="ff7 wse">=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span><span class="wsd">2</span></span><span class="ls3">,</span><span class="ff7 wsd">1)</span><span class="ws33">,<span class="blank"> </span>\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(0</span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7 wsd">3)</span><span class="ls38">,</span><span class="v2">\ue67e</span></span></span></div><div class="t m0 x3e h9 y7e ff6 fs0 fc0 sc0 ls16">t<span class="ff7 ls1 wse">=<span class="blank"> </span>(2</span><span class="ls3">,<span class="ff8 ls8">\u2212<span class="ff7 ls1">1)</span></span></span></div><div class="t m0 x3f h6 y7f ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls12">7</span><span class="ls1 ws10">\u2212<span class="ff7 ls12">6</span></span>\u2212<span class="ff7 ls12">5</span>\u2212<span class="ff7 ls12">4</span>\u2212<span class="ff7 ls12">3</span>\u2212<span class="ff7 ls12">2</span><span class="ls1 ws10">\u2212</span><span class="ff7 ls39 ws34">1<span class="blank"> </span>1234567<span class="blank _1e"></span></span></div><div class="t m0 xd h6 y80 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">6</span></div><div class="t m0 xd h6 y81 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">5</span></div><div class="t m0 xd h6 y82 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">4</span></div><div class="t m0 xd h6 y83 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">3</span></div><div class="t m0 xd h6 y84 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">2</span></div><div class="t m0 xd h6 y85 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">1</span></div><div class="t m0 xe h6 y86 ff7 fs2 fc0 sc0 ls1">1</div><div class="t m0 xe h6 y87 ff7 fs2 fc0 sc0 ls1">2</div><div class="t m0 xe h6 y88 ff7 fs2 fc0 sc0 ls1">3</div><div class="t m0 xe h6 y89 ff7 fs2 fc0 sc0 ls1">4</div><div class="t m0 xe h6 y8a ff7 fs2 fc0 sc0 ls1">5</div><div class="t m0 x40 h7 y8b ff6 fs2 fc0 sc0 ls1">x</div><div class="t m0 x10 h7 y8c ff6 fs2 fc0 sc0 ls1">y</div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>4<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf5" class="pf w0 h0" data-page-no="5"><div class="pc pc5 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w2 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg5.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x41 h6 y8d ff8 fs2 fc1 sc0 ls11">\u2212<span class="ff7 ls12">7</span>\u2212<span class="ff7 ls12">6</span><span class="ls1 ws10">\u2212<span class="ff7 ls12">5</span></span>\u2212<span class="ff7 ls12">4</span>\u2212<span class="ff7 ls12">3</span>\u2212<span class="ff7 ls12">2</span><span class="ls1 ws10">\u2212<span class="ff7 ws11">1<span class="blank _10"> </span>1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4<span class="blank"> </span>5<span class="blank"> </span>6<span class="blank"> </span>7</span></span></div><div class="t m0 x42 h6 y8e ff8 fs2 fc1 sc0 ls1 ws10">\u2212<span class="ff7">6</span></div><div class="t m0 x42 h6 y8f ff8 fs2 fc1 sc0 ls1 ws10">\u2212<span class="ff7">5</span></div><div class="t m0 x42 h6 y90 ff8 fs2 fc1 sc0 ls1 ws10">\u2212<span class="ff7">4</span></div><div class="t m0 x42 h6 y91 ff8 fs2 fc1 sc0 ls1 ws10">\u2212<span class="ff7">3</span></div><div class="t m0 x42 h6 y92 ff8 fs2 fc1 sc0 ls1 ws10">\u2212<span class="ff7">2</span></div><div class="t m0 x42 h6 y93 ff8 fs2 fc1 sc0 ls1 ws10">\u2212<span class="ff7">1</span></div><div class="t m0 x12 h6 y94 ff7 fs2 fc1 sc0 ls1">1</div><div class="t m0 x12 h6 y95 ff7 fs2 fc1 sc0 ls1">2</div><div class="t m0 x12 h6 y96 ff7 fs2 fc1 sc0 ls1">3</div><div class="t m0 x12 h6 y97 ff7 fs2 fc1 sc0 ls1">4</div><div class="t m0 x12 h6 y98 ff7 fs2 fc1 sc0 ls1">5</div><div class="c x43 y99 w4 h10"><div class="t m0 x4 h7 y9a ff6 fs2 fc1 sc0 ls1 ws35">\ue67e<span class="blank _13"></span>u</div><div class="t m0 x44 h7 y9b ff6 fs2 fc1 sc0 ls1 ws35">\ue67e<span class="blank _13"></span>u</div><div class="t m0 x25 h7 y9c ff6 fs2 fc1 sc0 ls1 ws35">\ue67e<span class="blank _13"></span>u</div><div class="t m0 x45 h7 y9d ff6 fs2 fc1 sc0 ls1 ws35">\ue67e<span class="blank _13"></span>u</div><div class="t m0 x42 h7 y9e ff6 fs2 fc1 sc0 ls1 ws35">\ue67e<span class="blank _13"></span>u</div><div class="t m0 x46 h7 y9f ff6 fs2 fc2 sc0 ls1 ws35">\ue67e<span class="blank _15"></span>v</div><div class="t m0 x47 h7 ya0 ff6 fs2 fc2 sc0 ls1 ws35">\ue67e<span class="blank _15"></span>v</div><div class="t m0 x19 h7 ya1 ff6 fs2 fc2 sc0 ls1 ws35">\ue67e<span class="blank _15"></span>v</div><div class="t m0 x48 h7 ya2 ff6 fs2 fc2 sc0 ls1 ws35">\ue67e<span class="blank _15"></span>v</div><div class="t m0 x49 h7 ya3 ff6 fs2 fc2 sc0 ls1 ws35">\ue67e<span class="blank _15"></span>v</div><div class="t m0 x4a h7 ya4 ff6 fs2 fc9 sc0 ls1 ws35">\ue67e<span class="blank _1f"></span>w</div><div class="t m0 x4b h7 ya5 ff6 fs2 fc9 sc0 ls1 ws35">\ue67e<span class="blank _1f"></span>w</div><div class="t m0 x4c h7 ya6 ff6 fs2 fc9 sc0 ls1 ws35">\ue67e<span class="blank _1f"></span>w</div><div class="t m0 x4d h7 ya7 ff6 fs2 fc9 sc0 ls1 ws35">\ue67e<span class="blank _1f"></span>w</div><div class="t m0 x2f h7 ya8 ff6 fs2 fc9 sc0 ls1 ws35">\ue67e<span class="blank _1f"></span>w</div><div class="t m0 x4e h7 ya9 ff6 fs2 fc4 sc0 ls1">\ue67e</div><div class="t m0 x4e h7 yaa ff6 fs2 fc4 sc0 ls1">t</div><div class="t m0 x4f h7 yab ff6 fs2 fc4 sc0 ls1">\ue67e</div><div class="t m0 x4f h7 yac ff6 fs2 fc4 sc0 ls1">t</div><div class="t m0 x50 h7 yad ff6 fs2 fc4 sc0 ls1">\ue67e</div><div class="t m0 x50 h7 yae ff6 fs2 fc4 sc0 ls1">t</div><div class="t m0 x23 h7 yaf ff6 fs2 fc4 sc0 ls1">\ue67e</div><div class="t m0 x23 h7 yb0 ff6 fs2 fc4 sc0 ls1">t</div><div class="t m0 x5 h7 yb1 ff6 fs2 fc4 sc0 ls1">\ue67e</div><div class="t m0 x5 h7 yb2 ff6 fs2 fc4 sc0 ls1">t</div><div class="t m0 x4a h7 yb3 ff6 fs2 fc1 sc0 ls1">O</div><div class="t m0 x4b h7 yb4 ff6 fs2 fc1 sc0 ls1">P</div><div class="t m0 x16 h7 yb5 ff6 fs2 fc1 sc0 ls1">Q</div><div class="t m0 x51 h7 yb6 ff6 fs2 fc1 sc0 ls1">R</div><div class="t m0 x52 h7 yb7 ff6 fs2 fc1 sc0 ls1">S</div></div><div class="t m0 x28 h7 yb8 ff6 fs2 fc1 sc0 ls1">x</div><div class="t m0 x1c h7 yb9 ff6 fs2 fc1 sc0 ls1">y</div><div class="t m0 x1 h2 yba ff1 fs0 fc0 sc0 ls1 ws36">11.<span class="blank _1d"> </span>Represente<span class="blank"> </span>os<span class="blank"> </span>v<span class="blank _2"></span>etores<span class="blank"> </span>no<span class="blank"> </span>espaço<span class="blank"> </span>euclidiano.<span class="blank _1d"> </span>Considere<span class="blank"> </span>que<span class="blank"> </span>a<span class="blank"> </span>origem<span class="blank"> </span>dos<span class="blank"> </span>vetores<span class="blank"> </span>e<span class="blank"> </span>a<span class="blank"> </span>origem<span class="blank"> </span>do<span class="blank"> </span>espaço<span class="blank"> </span>euclidiano</div><div class="t m0 xa h2 ybb ff1 fs0 fc0 sc0 ls1 ws0">sejam<span class="blank"> </span>coinciden<span class="blank _2"></span>tes.</div><div class="t m0 x1d h2 ybc ff1 fs0 fc0 sc0 ls1 ws13">(a)<span class="blank"> </span><span class="ff6 ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(1</span><span class="ls3">,</span><span class="ff7 wsd">2</span><span class="ls3">,</span><span class="ff7">3)</span></span></div><div class="t m0 x53 hb ybd ff6 fs0 fc0 sc0 ls1">y</div><div class="t m0 x1f hb ybe ff6 fs0 fc0 sc0 ls1">x</div><div class="t m0 x54 hb ybf ff6 fs0 fc0 sc0 ls1">z</div><div class="t m0 x55 h2 yc0 ff1 fs0 fc0 sc0 ls1 ws37">1<span class="blank"> </span>2</div><div class="t m0 x5 h2 yc1 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x5 h2 yc2 ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x5 h2 yc3 ff1 fs0 fc0 sc0 ls1">3</div><div class="t m0 x56 h2 yc4 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>5<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf6" class="pf w0 h0" data-page-no="6"><div class="pc pc6 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w2 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg6.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x57 hb yc5 ff6 fs0 fc1 sc0 ls1">y</div><div class="t m0 x58 hb yc6 ff6 fs0 fc1 sc0 ls1">x</div><div class="t m0 x59 hb yc7 ff6 fs0 fc1 sc0 ls1">z</div><div class="t m0 x1c hb yc8 ff6 fs0 fc2 sc0 ls1 wsd">\ue67e<span class="blank _12"></span>u</div><div class="t m0 x5a h2 yc9 ff1 fs0 fc1 sc0 ls1 ws37">1<span class="blank"> </span>2</div><div class="t m0 x12 h2 yca ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x12 h2 ycb ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x12 h2 ycc ff1 fs0 fc1 sc0 ls1">3</div><div class="t m0 x5b h2 ycd ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x1d h2 yce ff1 fs0 fc0 sc0 ls1 ws20">(b)<span class="blank"> </span><span class="ff6 ws21">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(2</span><span class="ls3">,</span><span class="ff7 wsd">4</span><span class="ls3">,</span><span class="ff7">1)</span></span></div><div class="t m0 x5c hb ycf ff6 fs0 fc0 sc0 ls1">y</div><div class="t m0 x5d hb yd0 ff6 fs0 fc0 sc0 ls1">x</div><div class="t m0 x5e hb yd1 ff6 fs0 fc0 sc0 ls1">z</div><div class="t m0 x36 h2 yd2 ff1 fs0 fc0 sc0 ls1 ws29">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4</div><div class="t m0 x5e h2 yd3 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x5e h2 yd4 ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x5f h2 yd5 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x13 h2 yd6 ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x60 hb yd7 ff6 fs0 fc1 sc0 ls1">y</div><div class="t m0 x61 hb yd8 ff6 fs0 fc1 sc0 ls1">x</div><div class="t m0 x62 hb yd9 ff6 fs0 fc1 sc0 ls1">z</div><div class="t m0 x63 h2 yda ff1 fs0 fc1 sc0 ls1 ws29">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4</div><div class="t m0 x62 h2 ydb ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x62 h2 ydc ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x27 h2 ydd ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x49 h2 yde ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x63 hb ydf ff6 fs0 fc4 sc0 ls1 wsd">\ue67e<span class="blank _13"></span>v</div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>6<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf7" class="pf w0 h0" data-page-no="7"><div class="pc pc7 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w2 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg7.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x1d h2 y28 ff1 fs0 fc0 sc0 ls1 ws38">(c)<span class="blank"> </span><span class="ff6 ws39">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff7 ws3a">=<span class="blank"> </span>(2</span><span class="ls3">,</span><span class="ff7 wsd">4</span><span class="ls3">,</span><span class="ff7 ws3b">1)<span class="blank"> </span><span class="ff1 ws3c">(Observ<span class="blank _2"></span>e<span class="blank"> </span>que<span class="blank"> </span>é<span class="blank"> </span>o<span class="blank"> </span>mesmo<span class="blank"> </span>vetor<span class="blank"> </span>do<span class="blank"> </span>item<span class="blank"> </span>(b).<span class="blank _20"> </span>Con<span class="blank _2"></span>tudo,<span class="blank _1d"> </span>a<span class="blank"> </span>construção<span class="blank"> </span>do<span class="blank"> </span>espaço<span class="blank"> </span>euclidiano<span class="blank"> </span>é</span></span></span></div><div class="t m0 x4c h2 y29 ff1 fs0 fc0 sc0 ls1 ws3d">diferen<span class="blank _2"></span>te.)</div><div class="t m0 x5c hb ye0 ff6 fs0 fc0 sc0 ls1">y</div><div class="t m0 x5d hb ye1 ff6 fs0 fc0 sc0 ls1">x</div><div class="t m0 x5e hb ye2 ff6 fs0 fc0 sc0 ls1">z</div><div class="t m0 x36 h2 ye3 ff1 fs0 fc0 sc0 ls1 ws29">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4</div><div class="t m0 x5e h2 ye4 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x5e h2 ye5 ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x64 h2 ye6 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x65 h2 ye7 ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x60 hb ye8 ff6 fs0 fc1 sc0 ls1">y</div><div class="t m0 x61 hb ye9 ff6 fs0 fc1 sc0 ls1">x</div><div class="t m0 x62 hb yea ff6 fs0 fc1 sc0 ls1">z</div><div class="t m0 x63 h2 yeb ff1 fs0 fc1 sc0 ls1 ws29">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4</div><div class="t m0 x62 h2 yec ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x62 h2 yed ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x56 h2 yee ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x66 h2 yef ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x63 hb yf0 ff6 fs0 fca sc0 ls1 wsd">\ue67e<span class="blank _13"></span>v</div><div class="t m0 x1d h2 yf1 ff1 fs0 fc0 sc0 ls1 ws3e">(d)<span class="blank"> </span><span class="ff6 ws24">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(4</span><span class="ls3">,</span><span class="ff7 wsd">3</span><span class="ls3">,</span><span class="ff7">2)</span></span></div><div class="t m0 x67 hb yf2 ff6 fs0 fc0 sc0 ls1">y</div><div class="t m0 x68 hb yf3 ff6 fs0 fc0 sc0 ls1">x</div><div class="t m0 x69 hb yf4 ff6 fs0 fc0 sc0 ls1">z</div><div class="t m0 x6a h2 yf5 ff1 fs0 fc0 sc0 ls1 ws3f">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4</div><div class="t m0 x69 h2 yf6 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x69 h2 yf7 ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x43 h2 yf8 ff1 fs0 fc0 sc0 ls1">4</div><div class="t m0 x6b h2 yf9 ff1 fs0 fc0 sc0 ls1">3</div><div class="t m0 x65 h2 yfa ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x37 h2 yfb ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>7<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf8" class="pf w0 h0" data-page-no="8"><div class="pc pc8 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w2 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg8.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x6c hb yfc ff6 fs0 fc1 sc0 ls1">y</div><div class="t m0 x50 hb yfd ff6 fs0 fc1 sc0 ls1">x</div><div class="t m0 x6d hb yc7 ff6 fs0 fc1 sc0 ls1">z</div><div class="t m0 x3e h2 yfe ff1 fs0 fc1 sc0 ls1 ws3f">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4</div><div class="t m0 x1c h2 yff ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x1c h2 y100 ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x2e h2 y101 ff1 fs0 fc1 sc0 ls1">4</div><div class="t m0 x14 h2 y102 ff1 fs0 fc1 sc0 ls1">3</div><div class="t m0 x66 h2 y103 ff1 fs0 fc1 sc0 ls1">2</div><div class="t m0 x6e h2 ycd ff1 fs0 fc1 sc0 ls1">1</div><div class="t m0 x12 hb y104 ff6 fs0 fcb sc0 ls1 wsd">\ue67e<span class="blank _16"></span>w</div><div class="t m0 x1 h2 y105 ff1 fs0 fc0 sc0 ls1 ws0">12.<span class="blank _1d"> </span>Dados<span class="blank"> </span>os<span class="blank"> </span>vetores<span class="blank"> </span>a<span class="blank"> </span>seguir,<span class="blank"> </span>determine<span class="blank"> </span>suas<span class="blank"> </span>componentes.</div><div class="t m0 x3f h6 y106 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls12">7</span>\u2212<span class="ff7 ls12">6</span><span class="ls1 ws10">\u2212<span class="ff7 ls12">5</span></span>\u2212<span class="ff7 ls12">4</span>\u2212<span class="ff7 ls12">3</span>\u2212<span class="ff7 ls12">2</span><span class="ls1 ws10">\u2212</span><span class="ff7 ls39 ws34">1<span class="blank"> </span>1234567<span class="blank _1e"></span></span></div><div class="t m0 xd h6 y107 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">6</span></div><div class="t m0 xd h6 y108 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">5</span></div><div class="t m0 xd h6 y109 ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">4</span></div><div class="t m0 xd h6 y10a ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">3</span></div><div class="t m0 xd h6 y10b ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">2</span></div><div class="t m0 xd h6 y10c ff8 fs2 fc0 sc0 ls11">\u2212<span class="ff7 ls1">1</span></div><div class="t m0 xe h6 y10d ff7 fs2 fc0 sc0 ls1">1</div><div class="t m0 xe h6 y10e ff7 fs2 fc0 sc0 ls1">2</div><div class="t m0 xe h6 y10f ff7 fs2 fc0 sc0 ls1">3</div><div class="t m0 xe h6 y110 ff7 fs2 fc0 sc0 ls1">4</div><div class="t m0 xe h6 y111 ff7 fs2 fc0 sc0 ls1">5</div><div class="c x6f y112 w4 h10"><div class="t m0 x70 h7 y113 ff6 fs2 fc0 sc0 ls1 ws35">\ue67e<span class="blank _13"></span>u</div><div class="t m0 x62 h7 y114 ff6 fs2 fc4 sc0 ls1 ws35">\ue67e<span class="blank _15"></span>v</div><div class="t m0 x71 h7 y115 ff6 fs2 fc2 sc0 ls1 ws35">\ue67e<span class="blank _1f"></span>w</div><div class="t m0 x35 h7 y116 ff6 fs2 fc9 sc0 ls1">\ue67e</div><div class="t m0 x72 h7 y117 ff6 fs2 fc9 sc0 ls1">t</div><div class="t m0 x52 h7 y118 ff6 fs2 fca sc0 ls1 ws35">\ue67e<span class="blank _21"></span>a</div><div class="t m0 x62 h7 y119 ff6 fs2 fc6 sc0 ls1">\ue67e</div><div class="t m0 x73 h7 y11a ff6 fs2 fc6 sc0 ls1">b</div></div><div class="t m0 x40 h7 y11b ff6 fs2 fc0 sc0 ls1">x</div><div class="t m0 x10 h7 y11c ff6 fs2 fc0 sc0 ls1">y</div><div class="t m0 x74 hf y11d ff6 fs0 fc1 sc0 ls1 ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(1</span><span class="ls3">,</span><span class="ff7 ws40">2)<span class="blank"> </span></span><span class="ws21">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(0</span><span class="ls3">,<span class="ff8 ls8">\u2212</span></span><span class="ff7 ws41">5)<span class="blank"> </span></span><span class="ws24">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(4</span><span class="lsb">,<span class="ff8 ls8">\u2212</span></span><span class="ff7 ws42">6)<span class="blank"> </span></span><span class="v2">\ue67e</span></span></span></div><div class="t m0 x75 h11 y11d ff6 fs0 fc1 sc0 ls16">t<span class="ff7 ls1 wse">=<span class="blank"> </span>(<span class="ff8 ls8">\u2212</span><span class="wsd">2</span></span><span class="ls3">,<span class="ff7 ls1 ws43">0)<span class="blank"> </span></span><span class="ls1 ws44">\ue67e<span class="blank _13"></span>a<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(1</span><span class="ls3">,</span><span class="ff7 ws45">2)<span class="blank"> </span></span><span class="v3">\ue67e</span></span></span></div><div class="t m0 x76 h9 y11d ff6 fs0 fc1 sc0 ls3a">b<span class="ff7 ls1 wse">=<span class="blank"> </span>(<span class="ff8 wsf">\u2212</span><span class="lsa">3</span></span><span class="ls3">,<span class="ff7 ls1">2)</span></span></div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>8<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pf9" class="pf w0 h0" data-page-no="9"><div class="pc pc9 w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w2 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bg9.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _0"> </span>Cálculo<span class="blank"> </span>Aplicado<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank"> </span>de<span class="blank"> </span>Pro<span class="blank _1"> </span>cessos</div><div class="t m0 x1 h2 y28 ff1 fs0 fc0 sc0 ls1 ws0">13.<span class="blank _1d"> </span>Dados<span class="blank"> </span>os<span class="blank"> </span>vetores<span class="blank"> </span>a<span class="blank"> </span>seguir,<span class="blank"> </span>determine<span class="blank"> </span>suas<span class="blank"> </span>componentes.</div><div class="t m0 x1e hb y11e ff6 fs0 fc0 sc0 ls1">x</div><div class="t m0 x28 hb y11f ff6 fs0 fc0 sc0 ls1">y</div><div class="t m0 x77 hb y120 ff6 fs0 fc0 sc0 ls1">z</div><div class="t m0 x20 hb y121 ff6 fs0 fc0 sc0 ls1 wsd">\ue67e<span class="blank _12"></span>u</div><div class="t m0 x78 hb y122 ff6 fs0 fc4 sc0 ls1 ws46">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="fc2 wsd">\ue67e<span class="blank _16"></span>w</span></div><div class="t m0 x3 hb y123 ff6 fs0 fc9 sc0 ls1">\ue67e</div><div class="t m0 x3 hb y124 ff6 fs0 fc9 sc0 ls1">t</div><div class="t m0 x6d h2 y125 ff1 fs0 fc0 sc0 ls1 ws47">1<span class="blank"> </span>2<span class="blank"> </span>3<span class="blank"> </span>4<span class="blank"> </span>5<span class="blank"> </span>6<span class="blank"> </span>7</div><div class="t m0 x77 h2 y126 ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x77 h2 y127 ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x77 h2 y128 ff1 fs0 fc0 sc0 ls1">3</div><div class="t m0 x77 h2 y129 ff1 fs0 fc0 sc0 ls1">4</div><div class="t m0 x77 h2 y12a ff1 fs0 fc0 sc0 ls1">5</div><div class="t m0 x77 h2 y12b ff1 fs0 fc0 sc0 ls1">6</div><div class="t m0 x79 h2 y12c ff1 fs0 fc0 sc0 ls1">1</div><div class="t m0 x61 h2 y12d ff1 fs0 fc0 sc0 ls1">2</div><div class="t m0 x7a h2 y12e ff1 fs0 fc0 sc0 ls1">3</div><div class="t m0 x74 hf y12f ff6 fs0 fc1 sc0 ls1 ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(1</span><span class="ls3">,<span class="ff7 lsa">5</span><span class="lsb">,</span></span><span class="ff7 ws48">6)<span class="blank"> </span></span><span class="ws17">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(2</span><span class="ls3">,</span><span class="ff7 wsd">0</span><span class="ls3">,</span><span class="ff7 ws49">4)<span class="blank"> </span></span><span class="ws1a">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="ff7 wse">=<span class="blank"> </span>(0</span><span class="ls3">,</span><span class="ff7 wsd">7</span><span class="ls3">,</span><span class="ff7 ws4a">2)<span class="blank"> </span></span><span class="v2">\ue67e</span></span></span></div><div class="t m0 x76 h9 y12f ff6 fs0 fc1 sc0 ls16">t<span class="ff7 ls1 wse">=<span class="blank"> </span>(3</span><span class="ls3">,<span class="ff7 ls1 wsd">6</span>,<span class="ff7 ls1">0)</span></span></div><div class="t m0 x1 h2 y27 ff1 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>01<span class="blank _e"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>9<span class="blank"> </span>de<span class="blank"> </span>9<span class="blank _f"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div> <div id="pfa" class="pf w0 h0" data-page-no="a"><div class="pc pca w0 h0"><img fetchpriority="low" loading="lazy" class="bi x0 y0 w5 h1" alt="" src="https://files.passeidireto.com/80832997-b696-4167-abaf-7782db8e84da/bga.png"><div class="t m0 x1 h12 y1 ff9 fs0 fc0 sc0 ls1 ws0">Engenharia<span class="blank"> </span>Química<span class="blank _22"> </span>Álgebra<span class="blank"> </span>Linear<span class="blank"> </span>e<span class="blank"> </span>Geometria<span class="blank"> </span>Analítica<span class="blank"> </span>Aplicados<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem</div><div class="t m0 x2 h3 y2 ffa fs1 fc0 sc0 ls1 ws1">CENTR<span class="blank _2"></span>O<span class="blank"> </span>UNIVERSITÁRIO<span class="blank"> </span>DE<span class="blank"> </span>TECNOLOGIA<span class="blank"> </span>DE</div><div class="t m0 x3 h3 y3 ffa fs1 fc0 sc0 ls1">CURITIBA</div><div class="t m0 x4 h13 y4 ffb fs1 fc0 sc0 ls1 ws2">Credenciada<span class="blank"> </span>p<span class="blank _1"> </span>ela<span class="blank"> </span>p<span class="blank _1"> </span>ortaria<span class="blank"> </span>do<span class="blank"> </span>MEC<span class="blank"> </span>n<span class="ffc ls0">º</span>1057<span class="blank"> </span>de<span class="blank"> </span>27/12/2021,</div><div class="t m0 x5 h13 y5 ffb fs1 fc0 sc0 ls1 ws2">publicada<span class="blank"> </span>no<span class="blank"> </span>DOU<span class="blank"> </span>em<span class="blank"> </span>28/12/2021</div><div class="t m0 x7b h13 y6 ffb fs1 fc0 sc0 ls1 ws2">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>02</div><div class="t m0 x6 h14 y130 ffb fs1 fc0 sc0 ls1 ws2">Disciplina:<span class="blank _3"> </span>Álgebra<span class="blank"> </span>Linear<span class="blank"> </span>e<span class="blank"> </span>Geometria<span class="blank"> </span>Analítica<span class="blank"> </span>Aplicados<span class="blank"> </span>a<span class="blank"> </span>Mo<span class="blank _1"> </span>delagem<span class="blank _23"> </span><span class="ws4b v0">NOT<span class="blank _5"></span>A:<span class="blank"> </span>Conhecimen<span class="blank _2"></span>to</span></div><div class="t m0 x6 h13 y8 ffb fs1 fc0 sc0 ls1 ws2">Professor:<span class="blank _3"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div><div class="t m0 x6 h13 y9 ffb fs1 fc0 sc0 ls1 ws3">Graduando(a):<span class="blank _24"> </span>Data:<span class="blank"> </span>/<span class="blank"> </span>/2023</div><div class="t m0 x6 h13 ya ffb fs1 fc0 sc0 ls1 ws4">Curso:<span class="blank _3"> </span>Engenharia<span class="blank _7"> </span>Química<span class="blank _25"> </span>P<span class="blank _2"></span>erío<span class="blank"> </span>do:</div><div class="t m0 x7 h12 yb ff9 fs0 fc0 sc0 ls1 ws0">1.<span class="blank _1d"> </span>Sobre<span class="blank"> </span>a<span class="blank"> </span>soma<span class="blank"> </span>geométrica<span class="blank"> </span>de<span class="blank"> </span>vetores,<span class="blank"> </span>está<span class="blank"> </span><span class="ffd ws4c">incorreta<span class="blank"> </span></span>a<span class="blank"> </span>seguin<span class="blank _2"></span>te<span class="blank"> </span>informação:</div><div class="t m0 x8 h12 yc ff9 fs0 fc0 sc0 ls1 ws4d">A.<span class="blank _1d"> </span>Nesse<span class="blank"> </span>tip<span class="blank _1"> </span>o<span class="blank"> </span>de<span class="blank"> </span>soma<span class="blank"> </span>de<span class="blank"> </span>vetores,<span class="blank"> </span>utiliza-se<span class="blank"> </span>sua<span class="blank"> </span>represen<span class="blank _2"></span>tação<span class="blank"> </span>geométrica<span class="blank"> </span>(seguimento<span class="blank"> </span>de<span class="blank"> </span>reta<span class="blank"> </span>orien<span class="blank _2"></span>tado)</div><div class="t m0 xb h12 y131 ff9 fs0 fc0 sc0 ls1 ws0">para<span class="blank"> </span>realizar<span class="blank"> </span>a<span class="blank"> </span>op<span class="blank _1"> </span>eração.</div><div class="t m0 x8 h12 y132 ff9 fs0 fc0 sc0 ls1 ws4e">B.<span class="blank _1d"> </span>Na<span class="blank"> </span>regra<span class="blank"> </span>do<span class="blank"> </span>p<span class="blank _1"> </span>olígono,<span class="blank _d"> </span>os<span class="blank"> </span>vetores<span class="blank"> </span>são<span class="blank"> </span>encadeados<span class="blank"> </span>de<span class="blank"> </span>forma<span class="blank"> </span>que<span class="blank"> </span>a<span class="blank"> </span>origem<span class="blank"> </span>de<span class="blank"> </span>um<span class="blank"> </span>v<span class="blank _2"></span>etor<span class="blank"> </span>coincida<span class="blank"> </span>com<span class="blank"> </span>a</div><div class="t m0 xb h12 y133 ff9 fs0 fc0 sc0 ls1 ws0">extremidade<span class="blank"> </span>de<span class="blank"> </span>outro<span class="blank"> </span>v<span class="blank _2"></span>etor.</div><div class="t m0 x9 h15 y134 ffd fs0 fc1 sc0 ls1 ws4f">C.<span class="blank _1d"> </span>T<span class="blank _5"></span>anto<span class="blank"> </span>a<span class="blank"> </span>regra<span class="blank"> </span>do<span class="blank"> </span>polígono<span class="blank"> </span>quanto<span class="blank"> </span>a<span class="blank"> </span>regra<span class="blank"> </span>do<span class="blank"> </span>paralelogramo<span class="blank"> </span>permitem<span class="blank"> </span>somar<span class="blank"> </span>quantos<span class="blank"> </span>v<span class="blank _2"></span>etores</div><div class="t m0 xb h15 y135 ffd fs0 fc1 sc0 ls1">quisermos.</div><div class="t m0 x8 h12 y11 ff9 fs0 fc0 sc0 ls1 ws50">D.<span class="blank _1d"> </span>Na<span class="blank"> </span>regra<span class="blank"> </span>do<span class="blank"> </span>paralelogramo,<span class="blank"> </span>as<span class="blank"> </span>origens<span class="blank"> </span>dos<span class="blank"> </span>vetores<span class="blank"> </span>somados<span class="blank"> </span>dev<span class="blank _2"></span>em<span class="blank"> </span>concorrer<span class="blank"> </span>(\u201cocupar\u201d)<span class="blank"> </span>o<span class="blank"> </span>mesmo<span class="blank"> </span>p<span class="blank _1"> </span>onto.</div><div class="t m0 x8 h12 y12 ff9 fs0 fc0 sc0 ls1 ws0">E.<span class="blank _1d"> </span>Usar<span class="blank"> </span>folhas<span class="blank"> </span>com<span class="blank"> </span>malhas<span class="blank"> </span>quadriculadas<span class="blank"> </span>auxiliam<span class="blank"> </span>na<span class="blank"> </span>soma<span class="blank"> </span>geométrica<span class="blank"> </span>de<span class="blank"> </span>vetores.</div><div class="t m0 x7 h12 y13 ff9 fs0 fc0 sc0 ls1 ws0">2.<span class="blank _1d"> </span>Sobre<span class="blank"> </span>a<span class="blank"> </span>intensidade<span class="blank"> </span>ou<span class="blank"> </span>módulo<span class="blank"> </span>de<span class="blank"> </span>um<span class="blank"> </span>vetor,<span class="blank"> </span>está<span class="blank"> </span><span class="ffd ws51">incorreto<span class="blank"> </span></span>a<span class="blank"> </span>seguin<span class="blank _2"></span>te<span class="blank"> </span>informação:</div><div class="t m0 x9 h15 y136 ffd fs0 fc1 sc0 ls1 ws5">A.<span class="blank _1d"> </span>O<span class="blank"> </span>sinal<span class="blank"> </span>da<span class="blank"> </span>intensidade<span class="blank"> </span>depende<span class="blank"> </span>do<span class="blank"> </span>sentido<span class="blank"> </span>do<span class="blank"> </span>v<span class="blank _2"></span>etor.</div><div class="t m0 x8 h16 y137 ff9 fs0 fc0 sc0 ls1 ws0">B.<span class="blank _1d"> </span>Dado<span class="blank"> </span>o<span class="blank"> </span>vetor<span class="blank"> </span><span class="ffe ws52">\ue67e<span class="blank _26"></span>p<span class="blank"> </span><span class="fff wse">=<span class="blank"> </span>(</span><span class="ws53">x,<span class="blank _27"> </span>y<span class="blank"> </span><span class="fff ls1b">)</span><span class="ff9 ws0">,<span class="blank"> </span>sua<span class="blank"> </span>in<span class="blank _2"></span>tensidade<span class="blank"> </span>é<span class="blank"> </span>calculado<span class="blank"> </span>como<span class="blank"> </span><span class="ffe ls3b">p<span class="fff ls3c">=<span class="ff10 ls3d v4">p</span></span><span class="ls3e">x<span class="ff11 fs3 ls3f v3">2</span><span class="fff ls18">+</span><span class="ls40">y</span></span></span><span class="ff11 fs3 v3">2</span></span></span></span></div><div class="t m0 x8 h12 y138 ff9 fs0 fc0 sc0 ls1 ws54">C.<span class="blank _1d"> </span>Dado<span class="blank"> </span>um<span class="blank _7"> </span>vetor<span class="blank"> </span><span class="ffe wsd">\ue67e<span class="blank _12"></span>u<span class="ff9 ws55">,<span class="blank"> </span>p<span class="blank _1"> </span>o<span class="blank _1"> </span>demos<span class="blank"> </span>representar<span class="blank"> </span>seu<span class="blank"> </span>módulo<span class="blank"> </span>como<span class="blank"> </span></span><span class="ls41">u</span><span class="ff9 ws56">ou<span class="blank"> </span><span class="ff12 wsf">|</span></span>\ue67e<span class="blank _12"></span>u<span class="ff12 ls42">|</span><span class="ff9 ws55">,<span class="blank"> </span>embora<span class="blank"> </span>seja<span class="blank"> </span>mais<span class="blank"> </span>recomendo<span class="blank"> </span>a<span class="blank"> </span>1<span class="ff13">ª</span></span></span></div><div class="t m0 xb h12 y139 ff9 fs0 fc0 sc0 ls1 ws3d">represen<span class="blank _2"></span>tação.</div><div class="t m0 x8 h16 y13a ff9 fs0 fc0 sc0 ls1 ws0">D.<span class="blank _1d"> </span>Dado<span class="blank"> </span>o<span class="blank"> </span>vetor<span class="blank _1c"> </span><span class="ffe ws57">\ue67e<span class="blank _12"></span>e<span class="blank"> </span><span class="fff wse">=<span class="blank"> </span>(</span><span class="ws58">x,<span class="blank _27"> </span>y<span class="blank"> </span>,<span class="blank _27"> </span>z<span class="blank _28"> </span><span class="fff wsd">)<span class="ff9 ws0">,<span class="blank"> </span>seu<span class="blank"> </span>mó<span class="blank _1"> </span>dulo<span class="blank"> </span>é<span class="blank"> </span>calculado<span class="blank"> </span>como<span class="blank"> </span></span></span><span class="ls43">e<span class="fff ls3c">=<span class="ff10 ls3d v4">p</span></span><span class="ls3e">x<span class="ff11 fs3 ls3f v3">2</span><span class="fff ls18">+</span><span class="ls40">y<span class="ff11 fs3 ls3f v3">2</span><span class="fff ls1a">+</span><span class="ls44">z</span></span></span></span><span class="ff11 fs3 v3">2</span></span></span></div><div class="t m0 x8 h12 y13b ff9 fs0 fc0 sc0 ls1 ws59">E.<span class="blank _1d"> </span>A<span class="blank"> </span>intensidade<span class="blank"> </span>do<span class="blank"> </span>v<span class="blank _2"></span>etor<span class="blank"> </span>represen<span class="blank _2"></span>ta<span class="blank"> </span>o<span class="blank"> </span>seu<span class="blank"> </span>v<span class="blank _2"></span>alor<span class="blank"> </span>n<span class="blank _2"></span>umérico.<span class="blank _29"> </span>O<span class="blank"> </span>T<span class="blank _5"></span>eorema<span class="blank"> </span>de<span class="blank"> </span>Pitágoras<span class="blank"> </span>p<span class="blank _1"> </span>o<span class="blank _1"> </span>de<span class="blank"> </span>nos<span class="blank"> </span>auxiliar<span class="blank"> </span>a</div><div class="t m0 xb h12 y13c ff9 fs0 fc0 sc0 ls1 ws0">lem<span class="blank _2"></span>brar<span class="blank"> </span>como<span class="blank"> </span>calculá-lo.</div><div class="t m0 x7 h12 y13d ff9 fs0 fc0 sc0 ls1 ws0">3.<span class="blank _1d"> </span>Sobre<span class="blank"> </span>os<span class="blank"> </span>vetores<span class="blank"> </span>no<span class="blank"> </span><span class="ffd wsd">plano</span>,<span class="blank"> </span>está<span class="blank"> </span><span class="ffd ws51">incorreto<span class="blank"> </span></span>a\ufb01rmar<span class="blank"> </span>que:</div><div class="t m0 x8 h12 y13e ff9 fs0 fc0 sc0 ls1 ws5a">A.<span class="blank _1d"> </span>sempre<span class="blank"> </span>p<span class="blank _1"> </span>o<span class="blank _1"> </span>demos<span class="blank"> </span>representá-los<span class="blank"> </span>como<span class="blank"> </span>soma<span class="blank"> </span>de<span class="blank"> </span>um<span class="blank"> </span>v<span class="blank _2"></span>etor<span class="blank"> </span>na<span class="blank"> </span>direção<span class="blank"> </span>horizon<span class="blank _2"></span>tal<span class="blank"> </span>e<span class="blank"> </span>um<span class="blank"> </span>v<span class="blank _2"></span>etor<span class="blank"> </span>na<span class="blank"> </span>direção</div><div class="t m0 xb h12 y13f ff9 fs0 fc0 sc0 ls1 ws3d">v<span class="blank _2"></span>ertical.</div><div class="t m0 x8 h12 y140 ff9 fs0 fc0 sc0 ls1 ws5b">B.<span class="blank _1d"> </span>o<span class="blank"> </span>mó<span class="blank _1"> </span>dulo<span class="blank"> </span>do<span class="blank"> </span>vetor<span class="blank"> </span>horizon<span class="blank _2"></span>tal<span class="blank"> </span>de<span class="blank"> </span>um<span class="blank"> </span>v<span class="blank _2"></span>etor<span class="blank"> </span>decomp<span class="blank _1"> </span>osto<span class="blank"> </span>é<span class="blank"> </span><span class="ffd ws5c">n<span class="blank _2"></span>umericamente<span class="blank"> </span><span class="ff9 ws5b">igual<span class="blank"> </span>à<span class="blank"> </span>componente<span class="blank"> </span>horizon<span class="blank _2"></span>tal</span></span></div><div class="t m0 xb h12 y141 ff9 fs0 fc0 sc0 ls1 ws9">do<span class="blank _18"> </span>vetor<span class="blank _18"> </span>decomposto.</div><div class="t m0 x8 h12 y142 ff9 fs0 fc0 sc0 ls1 ws5d">C.<span class="blank _1d"> </span>No<span class="blank"> </span>pro<span class="blank _1"> </span>cesso<span class="blank"> </span>de<span class="blank"> </span>decomp<span class="blank _1"> </span>osição<span class="blank"> </span>de<span class="blank"> </span>vetores,<span class="blank"> </span>po<span class="blank _1"> </span>de<span class="blank"> </span>ser<span class="blank"> </span>preciso<span class="blank"> </span>usar<span class="blank"> </span>as<span class="blank"> </span>razõ<span class="blank _1"> </span>es<span class="blank"> </span>trigonométricas<span class="blank"> </span>seno<span class="blank"> </span>e<span class="blank"> </span>cosseno</div><div class="t m0 xb h12 y143 ff9 fs0 fc0 sc0 ls1 ws0">de<span class="blank"> </span>algum<span class="blank"> </span>ângulo<span class="blank"> </span>in<span class="blank _2"></span>terno<span class="blank"> </span>do<span class="blank"> </span>triângulo<span class="blank"> </span>retângulo<span class="blank"> </span>gerado<span class="blank"> </span>nesse<span class="blank"> </span>pro<span class="blank _1"> </span>cesso.</div><div class="t m0 x45 h15 y144 ffd fs0 fc1 sc0 ls1 ws5e">D.<span class="blank _1d"> </span>No<span class="blank"> </span>pro<span class="blank _1"> </span>cesse<span class="blank"> </span>de<span class="blank"> </span>comp<span class="blank _1"> </span>osição,<span class="blank _9"> </span>para<span class="blank"> </span>determinar<span class="blank"> </span>as<span class="blank"> </span>comp<span class="blank _1"> </span>onen<span class="blank _2"></span>tes<span class="blank"> </span>de<span class="blank"> </span>um<span class="blank"> </span>vetor,<span class="blank"> </span>os<span class="blank"> </span>sinais<span class="blank"> </span>dev<span class="blank _2"></span>em</div><div class="t m0 xb h15 y145 ffd fs0 fc1 sc0 ls1 ws5">ser<span class="blank"> </span>ignorados.</div><div class="t m0 x8 h12 y146 ff9 fs0 fc0 sc0 ls1 ws5f">E.<span class="blank _1d"> </span>o<span class="blank"> </span>mó<span class="blank _1"> </span>dulo<span class="blank"> </span>do<span class="blank"> </span>vetor<span class="blank"> </span>v<span class="blank _2"></span>ertical<span class="blank"> </span>de<span class="blank"> </span>um<span class="blank"> </span>v<span class="blank _2"></span>etor<span class="blank"> </span>decomp<span class="blank _1"> </span>osto<span class="blank"> </span>é<span class="blank"> </span><span class="ffd ws60">n<span class="blank _2"></span>umericamen<span class="blank _2"></span>te<span class="blank"> </span><span class="ff9 ws5f">igual<span class="blank"> </span>à<span class="blank"> </span>comp<span class="blank _1"> </span>onente<span class="blank"> </span>v<span class="blank _2"></span>ertical<span class="blank"> </span>do</span></span></div><div class="t m0 xb h12 y147 ff9 fs0 fc0 sc0 ls1 ws9">v<span class="blank _2"></span>etor<span class="blank _18"> </span>decomp<span class="blank"> </span>osto.</div><div class="t m0 x7 h12 y148 ff9 fs0 fc0 sc0 ls1 ws6">4.<span class="blank"> </span>Calcule:</div><div class="t m0 x1d h12 y149 ff9 fs0 fc0 sc0 ls1 ws13">(a)<span class="blank"> </span><span class="ffe ws61">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="fff ls45">+</span><span class="ws62">\ue67e<span class="blank _13"></span>v<span class="blank"> </span><span class="ff9 ws9">sab<span class="blank"> </span>endo<span class="blank _18"> </span>que<span class="blank _18"> </span></span><span class="ws14">\ue67e<span class="blank _12"></span>u<span class="blank"> </span><span class="fff wse">=<span class="blank"> </span>(1</span><span class="ls3">,</span><span class="fff ws27">9)<span class="blank"> </span><span class="ff9 ls46">e</span></span><span class="ws21">\ue67e<span class="blank _12"></span>v<span class="blank"> </span><span class="fff wse">=<span class="blank"> </span>(3</span><span class="ls3">,</span><span class="fff">1)</span></span></span></span></span></div><div class="t m0 x1d h17 y14a ff9 fs0 fc0 sc0 ls1 ws63">(b)<span class="blank"> </span><span class="ffe ws64">\ue67e<span class="blank _13"></span>a<span class="blank"> </span><span class="fff ls47">+</span><span class="v2">\ue67e</span></span></div><div class="t m0 x50 h17 y14a ffe fs0 fc0 sc0 ls48">t<span class="ff9 ls1 ws9">sab<span class="blank"> </span>endo<span class="blank _18"> </span>que<span class="blank _1c"> </span></span><span class="ls1 ws44">\ue67e<span class="blank _13"></span>a<span class="blank"> </span><span class="fff wse">=<span class="blank"> </span>(0</span><span class="ls3">,</span><span class="fff ws27">7)<span class="blank"> </span><span class="ff9 ls49">e</span></span><span class="v2">\ue67e</span></span></div><div class="t m0 x7b h9 y14a ffe fs0 fc0 sc0 ls16">t<span class="fff ls1 wse">=<span class="blank"> </span>(<span class="ff12 ls8">\u2212</span><span class="wsd">8</span></span><span class="ls3">,<span class="fff ls1">3)</span></span></div><div class="t m0 x1d h12 y14b ff9 fs0 fc0 sc0 ls1 ws19">(c)<span class="blank"> </span><span class="ffe ws65">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="fff ls4a">+</span><span class="ws66">\ue67e<span class="blank _12"></span>z<span class="blank"> </span><span class="ff9 ws9">sab<span class="blank"> </span>endo<span class="blank _18"> </span>que<span class="blank _1d"> </span></span><span class="ws1a">\ue67e<span class="blank _16"></span>w<span class="blank"> </span><span class="fff wse">=<span class="blank"> </span>(3</span><span class="ls3">,<span class="ff12 ls8">\u2212</span></span><span class="fff wsd">1</span><span class="ls3">,</span><span class="fff ws27">7)<span class="blank"> </span><span class="ff9 ls4b">e</span></span><span class="ws67">\ue67e<span class="blank _12"></span>z<span class="blank"> </span><span class="fff wse">=<span class="blank"> </span>(8</span><span class="ls3">,<span class="ff12 ls8">\u2212</span></span><span class="fff wsd">2</span><span class="ls3">,<span class="ff12 ls8">\u2212</span></span><span class="fff">5)</span></span></span></span></span></div><div class="t m0 x1 h12 y27 ff9 fs0 fc0 sc0 ls1 ws0">Lista<span class="blank"> </span>de<span class="blank"> </span>Exercícios<span class="blank"> </span>\u2013<span class="blank"> </span>Encon<span class="blank _2"></span>tro<span class="blank"> </span>02<span class="blank _2a"> </span>P<span class="blank _2"></span>ágina<span class="blank"> </span>1<span class="blank"> </span>de<span class="blank"> </span>13<span class="blank _2b"> </span>Professor:<span class="blank _d"> </span>Marcelo<span class="blank"> </span>Keiji<span class="blank"> </span>Saito</div></div><div class="pi" data-data="{"ctm":[1.000000,0.000000,0.000000,1.000000,0.000000,0.000000]}"></div></div>
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