<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/1efad4e3-43b6-46ba-b952-73f2082df773/bg1.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h2 y3 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="c x3 y4 w2 h3"><div class="t m0 x4 h4 y5 ff1 fs1 fc0 sc0 ls0">1<span class="fs2 ls2 wsa"> </span></div></div><div class="t m0 x5 h5 y6 ff2 fs3 fc0 sc0 ls2 wsa">AVI <span class="ff3 ws0">\u2013</span> AVALIAÇÃO INTEGRADA </div><div class="t m0 x6 h5 y7 ff2 fs3 fc0 sc0 ls2 wsa">FOLHA DE RESPOSTA </div><div class="t m0 x1 h5 y8 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h5 y9 ff2 fs3 fc0 sc0 ls2 wsa"><span class="fc4 sc0">Di</span><span class="fc4 sc0">sci</span><span class="fc4 sc0"> </span></div><div class="t m0 x2 h5 ya ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="c x7 yb w3 h6"><div class="t m0 x8 h7 yc ff2 fs4 fc1 sc0 ls2 wsa">INFORMAÇÕES IMPORTANTES! LEIA ANTES DE IN<span class="blank _0"></span>ICIAR!<span class="blank _1"> </span><span class="ff1"> </span></div></div><div class="c x7 yd w3 h8"><div class="t m0 x9 h9 ye ff1 fs1 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h9 yf ff1 fs1 fc0 sc0 ls2 wsa">A Avaliação Int<span class="blank _0"></span>egrada (<span class="ls3 ws1">AV<span class="ls1">I</span></span><span class="ls4">) </span>é uma at<span class="blank _0"></span>ividade q<span class="blank _0"></span>ue compree<span class="blank _0"></span>nde resolução de cál<span class="blank _0"></span>culo. </div><div class="t m0 x9 h9 y10 ff1 fs1 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h9 y11 ff1 fs1 fc0 sc0 ls2 wsa">Esta avaliaç<span class="blank _0"></span>ão vale até <span class="ls0">10</span>,0 po<span class="blank _0"></span>ntos. </div><div class="t m0 x9 h9 y12 ff1 fs1 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 ha y13 ff1 fs0 fc2 sc0 ls2 ws2">Atenção<span class="fs5 ws3 v1">1</span><span class="wsa">: Serão con<span class="blank _1"> </span>sideradas par<span class="blank _1"> </span><span class="ff4">a avaliação soment<span class="blank _1"> </span>e as atividades <span class="blank _1"> </span>com status \u201c<span class="blank _1"> </span>enviado\u201d. As ati<span class="blank _1"> </span>vidades com </span></span></div><div class="t m0 x9 h2 y14 ff4 fs0 fc2 sc0 ls2 wsa">status na forma de \u201cras<span class="blank _1"> </span>cunho\u201d não serão co<span class="blank _1"> </span><span class="ff1">rrigidas. L<span class="blank _1"> </span>embre-</span>se de clicar <span class="blank _1"> </span>no botão \u201cenviar\u201d.<span class="blank _1"> </span><span class="ff1"> </span></div><div class="t m0 x9 hb y15 ff2 fs1 fc1 sc0 ls2 wsa"> </div><div class="t m0 x9 hb y16 ff2 fs1 fc1 sc0 ls2 ws4">Atenção<span class="fs6 ws5 v2">2</span><span class="ls5 wsa">: <span class="ff1 fc0 ls2">A atividade<span class="blank _0"></span> deve ser<span class="blank _0"></span> postada somente nest<span class="blank _0"></span>e modelo de Folha<span class="blank _0"></span> de Respostas<span class="blank _0"></span>,<span class="fc1"> p</span>referencialment<span class="blank _0"></span>e, na versão <span class="ff2 fc3 ls6 ws6">Pd<span class="ls2 ws4">f</span></span><span class="ls7">. </span> </span></span></div><div class="t m0 x9 h9 y17 ff1 fs1 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 hb y18 ff2 fs1 fc2 sc0 ls2 wsa">Impo<span class="blank _0"></span>rtan<span class="blank _0"></span>te: </div><div class="t m0 x9 h2 y19 ff1 fs0 fc2 sc0 ls2 wsa">Nunca <span class="blank _2"> </span>copie <span class="blank _2"> </span>e <span class="blank _2"> </span>cole <span class="blank _2"> </span>informações <span class="blank _3"> </span><span class="ls8 ws7">da</span> <span class="blank _4"> </span>internet, <span class="blank _2"> </span><span class="ls8 ws7">de</span> <span class="blank _4"> </span>outro <span class="blank _2"> </span>colega <span class="blank _4"> </span><span class="ls9 ws8">ou</span> <span class="blank _2"> </span>qualquer <span class="blank _4"> </span>outra <span class="blank _2"> </span>fonte, <span class="blank _4"> </span>como <span class="blank _4"> </span>se<span class="blank _0"></span>ndo <span class="blank _4"> </span>sua </div><div class="t m0 x9 h2 y1a ff1 fs0 fc2 sc0 ls2 wsa">produção, <span class="blank _2"> </span><span class="lsa ws9">já</span> <span class="blank _5"> </span>que <span class="blank"> </span>es<span class="blank _0"></span>sas <span class="blank _4"> </span>situações <span class="blank"> </span>c<span class="blank _0"></span>aracter<span class="blank _0"></span>izam <span class="blank _4"> </span>plágio e <span class="blank"> </span>i<span class="blank _0"></span>nvalid<span class="blank _0"></span>am <span class="blank _4"> </span>sua <span class="blank"> </span>ativ<span class="blank _0"></span>idade.<span class="blank _0"></span> </div><div class="t m0 x9 h2 y1b ff1 fs0 fc2 sc0 ls2 wsa"> </div><div class="t m0 x9 h9 y1c ff1 fs1 fc0 sc0 ls2 wsa">Se for<span class="blank _0"></span> pedi<span class="blank _0"></span>do <span class="blank _0"></span>na<span class="blank _0"></span> ati<span class="blank _0"></span>vidade<span class="blank _0"></span>, <span class="blank _0"></span>colo<span class="blank _0"></span>que as<span class="blank _0"></span> refe<span class="blank _0"></span>rênc<span class="blank _0"></span>ias <span class="blank _0"></span>bibl<span class="blank _0"></span>io<span class="blank _0"></span>gráfi<span class="blank _0"></span>cas p<span class="blank _0"></span>ar<span class="blank _0"></span>a não<span class="blank _0"></span> pe<span class="blank _0"></span>rder <span class="blank _0"></span>pont<span class="blank _0"></span>o. </div><div class="t m0 x9 hc yc ff1 fs4 fc0 sc0 ls2 wsa"> </div></div><div class="t m0 x2 h5 y1d ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="c x7 y1e w4 hd"><div class="t m0 xa h7 y1f ff2 fs4 fc1 sc0 ls2 wsa"> </div></div><div class="c x7 y20 w4 he"><div class="t m0 x8 h7 y21 ff2 fs4 fc1 sc0 ls2 wsa">CRITÉRIOS PARA AVALIAÇÃO DAS ATIVIDADES - CÁLCULO </div><div class="t m0 x9 hc y22 ff1 fs4 fc0 sc0 ls2 wsa"> </div><div class="t m0 xb hb y23 ff2 fs1 fc0 sc0 ls2 wsa">Caminho de Resolução:<span class="ff1"> O trabalho deve seguir uma linha <span class="blank _1"> </span>de raciocínio e coerência do início ao fim. <span class="blank _1"> </span>O aluno deve colocar todo </span></div><div class="t m0 xb h9 y24 ff1 fs1 fc0 sc0 ls2 wsa">o desenvo<span class="blank _0"></span>lvimento da ati<span class="blank _0"></span>vidade até chegar ao r<span class="blank _0"></span>esultado<span class="blank _0"></span> final. </div><div class="t m0 xb h9 y25 ff1 fs1 fc0 sc0 ls2 wsa"> </div><div class="t m0 xb hb y26 ff2 fs1 fc0 sc0 ls2 wsa">Resultado Final<span class="blank _0"></span>:<span class="ff1"> A resoluç<span class="blank _0"></span>ão do exercíci<span class="blank _0"></span>o deve levar ao re<span class="blank _0"></span>sultado final c<span class="blank _0"></span>orreto. </span></div><div class="t m0 xb h9 y27 ff1 fs1 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h9 y28 ff1 fs1 fc0 sc0 ls2 wsa">A <span class="blank _1"> </span>AVI <span class="blank _1"> </span>que <span class="blank _1"> </span>possui <span class="blank _1"> </span>detalha<span class="blank _0"></span>mento do <span class="blank _1"> </span>cálculo <span class="blank _1"> </span>realizado, sem <span class="blank _1"> </span>pular <span class="blank _1"> </span>nenhuma <span class="blank _1"> </span>etapa, <span class="blank _1"> </span>e <span class="blank _1"> </span>apresentar<span class="blank _0"></span> <span class="blank _1"> </span>resultado <span class="blank _1"> </span>final correto <span class="blank _1"> </span>receberá nota <span class="blank _1"> </span>10<span class="blank _1"> </span>. <span class="blank _1"> </span>A </div><div class="t m0 x9 h9 y29 ff1 fs1 fc0 sc0 ls2 wsa">atividade<span class="blank _0"></span> <span class="blank _1"> </span>que <span class="blank _1"> </span>apresent<span class="blank _0"></span>ar <span class="blank _1"> </span>apenas <span class="blank _1"> </span>result<span class="blank _0"></span>ado <span class="blank _1"> </span>final, mesmo <span class="blank _1"> </span>que <span class="blank _1"> </span>correto, sem <span class="blank _1"> </span>inserir as <span class="blank _1"> </span>etapas <span class="blank _1"> </span>do <span class="blank _1"> </span>cálculo receberá <span class="blank _1"> </span>nota zero.<span class="blank _1"> </span> <span class="blank _1"> </span>Os <span class="blank _1"> </span>erros serão </div><div class="t m0 x9 h9 y2a ff1 fs1 fc0 sc0 ls2 wsa">descontad<span class="blank _0"></span>os de acordo<span class="blank _0"></span> com a sua relevânci<span class="blank _0"></span>a. </div></div><div class="t m0 x2 h4 y2b ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y2c ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y2d ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y2e ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y2f ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y30 ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y31 ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y32 ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y33 ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h4 y34 ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="c xc y35 w5 hf"><div class="t m0 xd h10 y36 ff2 fs2 fc0 sc0 ls2 wsa">Disciplina: Geomet<span class="blank _0"></span>ria Anal<span class="blank _0"></span>ítica e Álgeb<span class="blank _0"></span>ra Linear - EAD.<span class="ff1"> </span></div></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 w1 h1" alt="" src="https://files.passeidireto.com/1efad4e3-43b6-46ba-b952-73f2082df773/bg2.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h2 y3 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="c x3 y4 w2 h3"><div class="t m0 x4 h4 y5 ff1 fs1 fc0 sc0 ls0">2<span class="fs2 ls2 wsa"> </span></div></div><div class="c x7 y37 w6 h11"><div class="t m0 x9 h5 y38 ff2 fs3 fc0 sc0 ls2 wsa">Resolução / Resposta<span class="ff1"> </span></div></div><div class="c x7 y39 w6 h12"><div class="t m0 x9 h5 y3a ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y3b ff2 fs3 fc0 sc0 ls2 wsa">QUESTÃO 01 </div><div class="t m0 x9 h5 y3c ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y3d ff2 fs3 fc0 sc0 ls2 wsa">Ângulo de lançamento </div><div class="t m0 x9 h5 y3e ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y3f ff1 fs3 fc0 sc0 ls2 wsa">Um engenheiro fez o levantamento de uma regiã<span class="blank _0"></span>o demarcando os pontos fundamentais A </div><div class="t m0 x9 h13 y40 ff1 fs3 fc0 sc0 ls2 wsa">(1, -5, 9), B (-3, 4, 8) e C (7, 1, 6), com o propósito de determinar as coordenadas dos </div><div class="t m0 x9 h13 y41 ff1 fs3 fc0 sc0 ls2 wsa">vetores, os módulos respectivos e o valor do cosseno do ângulo determinado pelos dois<span class="blank _0"></span> </div><div class="t m0 x9 h13 y42 ff1 fs3 fc0 sc0 ls2 wsa">vetores, com o objetivo de estudar o desempenho de um determinado corpo que se </div><div class="t m0 x9 h13 y43 ff1 fs3 fc0 sc0 ls2 wsa">desloca do ponto B ao A e depois do B ao C. </div><div class="t m0 x9 h5 y44 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y45 ff2 fs3 fc0 sc0 ls2 wsa">Colaborando com esse engenheiro, desenvolva cada<span class="blank _0"></span> item a seguir:<span class="blank _1"> </span> </div><div class="t m0 x9 h5 y46 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y47 ff2 fs3 fc0 sc0 ls2 wsa">a) Apresente as coordenadas dos vetores indicados e o mó<span class="blank _0"></span>dulo de cada<span class="blank _1"> </span> vetor indicado. </div><div class="t m0 x9 h5 y48 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y49 ff1 fs3 fc0 sc0 ls2 wsa">Para a resolução, deve-se considerar a utilização das três coordenadas: </div><div class="t m0 x9 h13 y4a ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y4b ff1 fs3 fc0 sc0 ls2 wsa">A = (1, -5, 9) </div><div class="t m0 x9 h13 y4c ff1 fs3 fc0 sc0 ls2 wsa">B = (-3, 4, 8) </div><div class="t m0 x9 h13 y4d ff1 fs3 fc0 sc0 ls2 wsa">C = (7, 1, 6) </div><div class="t m0 x9 h13 y4e ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y4f ff1 fs3 fc0 sc0 ls2 wsa">Deve se encontrar dois vetores o </div><div class="t m0 x9 h13 y50 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y51 ff1 fs3 fc0 sc0 ls2 wsa">u = BA </div><div class="t m0 x9 h13 y52 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y53 ff1 fs3 fc0 sc0 ls2 wsa">v = BC </div><div class="t m0 x9 h13 y54 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y55 ff1 fs3 fc0 sc0 ls2 wsa">Deste modo o vetor u será descrito: </div><div class="t m0 x9 h13 y56 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y57 ff1 fs3 fc0 sc0 ls2 wsa">u = BA = A-B = Xa <span class="ff4 lsb">\u2013</span> Xb, Ya <span class="ff4 lsb">\u2013</span> Yb, Za = Zb </div><div class="t m0 x9 h13 y58 ff1 fs3 fc0 sc0 ls2 wsa">u = 1 <span class="ff4 ws0">\u2013</span> (-3), (-5) <span class="ff4 lsb">\u2013</span> 4, 9 <span class="ff4 lsb">\u2013</span> 8 </div><div class="t m0 x9 h13 y59 ff1 fs3 fc0 sc0 ls2 wsa">u = (4, -9, 1) </div><div class="t m0 x9 h13 y5a ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y5b ff1 fs3 fc0 sc0 ls2 wsa">Essas são as coordenadas do vetor u. </div><div class="t m0 x9 h13 y5c ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y5d ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y5e ff1 fs3 fc0 sc0 ls2 wsa">A resolução para o vetor v será: </div><div class="t m0 x9 h13 y5f ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y60 ff1 fs3 fc0 sc0 ls2 wsa">v = BC = C <span class="ff4 ws0">\u2013</span> B </div><div class="t m0 x9 h13 y61 ff1 fs3 fc0 sc0 ls2 wsa">v = Xc <span class="ff4 ws0">\u2013</span> Xb, Yc <span class="ff4 ws0">\u2013</span> Yb, Zc - <span class="lsb wsb">Zb</span> </div><div class="t m0 x9 h13 y62 ff1 fs3 fc0 sc0 ls2 wsa">v = (7 <span class="ff4 ws0">\u2013</span> (-3), 1 <span class="ff4 ws0">\u2013</span> 4, 6 <span class="ff4 ws0">\u2013</span><span class="lsc"> <span class="lsd wsc">8)</span></span> </div><div class="t m0 x9 h13 y63 ff1 fs3 fc0 sc0 ls2 wsa">v = (10, -3, -2) </div><div class="t m0 x9 h13 y64 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y65 ff1 fs3 fc0 sc0 ls2 wsa">Essas são as coordenadas do <span class="blank _1"> </span>vetor v. </div><div class="t m0 x9 h5 y66 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y67 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y68 ff2 fs3 fc0 sc0 ls2 wsa"> </div></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 w1 h1" alt="" src="https://files.passeidireto.com/1efad4e3-43b6-46ba-b952-73f2082df773/bg3.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h2 y3 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="c x3 y4 w2 h3"><div class="t m0 x4 h4 y5 ff1 fs1 fc0 sc0 ls0">3<span class="fs2 ls2 wsa"> </span></div></div><div class="c x7 y69 w6 h14"><div class="t m0 x9 h13 y6a ff1 fs3 fc0 sc0 ls2 wsa">Para resolução do módulo de cada vetor, eleva-se ao quadrado: </div><div class="t m0 x9 h13 y6b ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y6c ff1 fs3 fc0 sc0 ls2 wsa">Para o vetor u o módulo será: </div><div class="t m0 x9 h13 y6d ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y6e ff4 fs3 fc0 sc0 ls2 wsa">|u| = \u221a(4)² + (<span class="ff1">-9)² + (1)² </span></div><div class="t m0 x9 h5 y6f ff4 fs3 fc0 sc0 ls2 wsa">|u| = \u221a16 + 81 + 1<span class="ff2"> </span></div><div class="t m0 x9 h5 y70 ff4 fs3 fc0 sc0 ls2 wsa">|u| = \u221a98<span class="ff2"> </span></div><div class="t m0 x9 h5 y71 ff1 fs3 fc0 sc0 ls2 wsa">|u| = 9,89<span class="ff2"> </span></div><div class="t m0 x9 h5 y72 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y73 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y74 ff1 fs3 fc0 sc0 ls2 wsa">Já para o vetor v, o módulo será conforme abaixo: </div><div class="t m0 x9 h13 y75 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y76 ff4 fs3 fc0 sc0 ls2 wsa">|v| = \u221a(1<span class="ff1">0)² + (-3)² + (-2)² </span></div><div class="t m0 x9 h13 y77 ff4 fs3 fc0 sc0 ls2 wsa">|v| = \u221a100 + 9 + 4<span class="ff1"> </span></div><div class="t m0 x9 h13 y78 ff4 fs3 fc0 sc0 ls2 wsa">|v| = \u221a110<span class="ff1"> </span></div><div class="t m0 x9 h13 y79 ff1 fs3 fc0 sc0 ls2 wsa">|v| = 10,48 </div><div class="t m0 x9 h13 y7a ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y7b ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y7c ff3 fs3 fc0 sc0 ls2 wsa">b) Calcule o valor do cos \u03b2, sendo \u03b2 a medida<span class="blank _0"></span> do ângulo determinado pel<span class="blank _0"></span>os dois vetores.<span class="blank _1"> </span><span class="ff2"> </span></div><div class="t m0 x9 h13 y7d ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y7e ff1 fs3 fc0 sc0 ls2 wsa">Para este caso, utilizaremos a operação para vet<span class="blank _0"></span>ores, produto escalar definida para </div><div class="t m0 x9 h13 y7f ff1 fs3 fc0 sc0 ls2 wsa">vetores no R<span class="lse wsd">³:</span> </div><div class="t m0 x9 h13 y80 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y81 ff1 fs3 fc0 sc0 ls2 wsa">Deve-se multiplicar os vetores, no caso u . v </div><div class="t m0 x9 h13 y82 ff1 fs3 fc0 sc0 ls2 wsa">= 4 . 10 + (-9) . (-3) +1 . (-<span class="lsd wsc">2)</span> </div><div class="t m0 x9 h13 y83 ff1 fs3 fc0 sc0 ls2 wsa">= 40 + 27 <span class="ff4 ws0">\u2013</span> 2 </div><div class="t m0 x9 h13 y84 ff1 fs3 fc0 sc0 ls2 wsa">= 65 </div><div class="t m0 x9 h13 y85 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y86 ff1 fs3 fc0 sc0 ls2 wsa">Utiliza-se essa operação, pois é uma das propriedades que dado o ângulo <span class="blank _6"> </span> entre dois </div><div class="t m0 x9 h13 y87 ff1 fs3 fc0 sc0 ls2 wsa">vetores <span class="blank _7"> </span> <span class="lsf">e <span class="blank _8"> </span></span>: </div><div class="t m0 x9 h13 y88 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 xe h13 y89 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h15 y8a ff1 fs7 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y8b ff1 fs3 fc0 sc0 ls2 wsa">Assim, para nossos vetores: </div><div class="t m0 x9 h4 y8c ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 xe h4 y8d ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 xf h13 y8e ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y5f ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y60 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y61 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y62 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y63 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y64 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y65 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y8f ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y67 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y68 ff2 fs3 fc0 sc0 ls2 wsa"> </div></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 w1 h1" alt="" src="https://files.passeidireto.com/1efad4e3-43b6-46ba-b952-73f2082df773/bg4.png"><div class="t m0 x1 h2 y1 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h2 y2 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="t m0 x2 h2 y3 ff1 fs0 fc0 sc0 ls2 wsa"> </div><div class="c x3 y4 w2 h3"><div class="t m0 x4 h4 y5 ff1 fs1 fc0 sc0 ls0">4<span class="fs2 ls2 wsa"> </span></div></div><div class="c x7 y90 w6 h16"><div class="t m0 x9 h5 y91 ff2 fs3 fc0 sc0 ls2 wsa">QUESTÃO 02 </div><div class="t m0 x9 h13 y92 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 y93 ff1 fs3 fc0 sc0 ls2 wsa">A <span class="blank _9"> </span>Geometria <span class="blank _9"> </span>Euclidiana <span class="blank _9"> </span>con<span class="ff4">siste <span class="blank _9"> </span>num <span class="blank _9"> </span>sistema <span class="blank _9"> </span>de <span class="blank _9"> </span>axiomas <span class="blank _9"> </span>\u201cbastante\u201d <span class="blank _9"> </span>naturais. <span class="blank _9"> </span>O <span class="blank _9"> </span>mais </span></div><div class="t m0 x9 h13 y94 ff1 fs3 fc0 sc0 ls2 wsa">importante <span class="blank _1"> </span>destes <span class="blank _1"> </span>axiomas <span class="blank _1"> </span>é <span class="blank _a"> </span>o <span class="blank _1"> </span>postulado <span class="blank _1"> </span>das <span class="blank _1"> </span>paralelas: <span class="blank _a"> </span>Dada <span class="blank _1"> </span>uma <span class="blank _1"> </span>reta <span class="blank _1"> </span>L <span class="blank _1"> </span>e <span class="blank _a"> </span>um <span class="blank _1"> </span>ponto <span class="blank _1"> </span>fora </div><div class="t m0 x9 h13 y95 ff1 fs3 fc0 sc0 ls2 wsa">desta reta, existe uma única reta R passando por este ponto e que não intersecta a reta L. </div><div class="t m0 x9 h13 y96 ff1 fs3 fc0 sc0 ls2 wsa">Fonte: <span class="blank _b"> </span>IME <span class="blank _b"> </span>USP. <span class="blank _b"> </span>Dis<span class="blank _0"></span>ponível <span class="blank _b"> </span>em: <span class="blank _b"> </span><https://www.ime.usp.br/>. <span class="blank _b"> </span>Acesso <span class="blank _b"> </span>em: <span class="blank _b"> </span>j<span class="blank _0"></span>ul. <span class="blank _b"> </span>2020. </div><div class="t m0 x9 h13 y97 ff1 fs3 fc0 sc0 ls2 wsa">Adaptado. </div><div class="t m0 x9 h13 y98 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y99 ff2 fs3 fc0 sc0 ls2 wsa">Quando <span class="blank _4"> </span>estudamos <span class="blank _2"> </span>a <span class="blank _4"> </span>reta, <span class="blank _4"> </span>seja <span class="blank _4"> </span>no <span class="blank _4"> </span>R² <span class="blank _4"> </span>ou <span class="blank _4"> </span>no <span class="blank _4"> </span>R³, <span class="blank _4"> </span>é <span class="blank _4"> </span>fund<span class="blank _1"> </span>amental <span class="blank _2"> </span>co<span class="blank _1"> </span>nhecermos <span class="blank _2"> </span>um <span class="blank _4"> </span>dos </div><div class="t m0 x9 h5 y9a ff2 fs3 fc0 sc0 ls2 wsa">axiomas <span class="blank _4"> </span>da <span class="blank _4"> </span>Geometria <span class="blank _4"> </span>Euclidiana <span class="blank _4"> </span>que <span class="blank _4"> </span>afi<span class="blank _1"> </span>rma: <span class="blank _4"> </span>dois <span class="blank _9"> </span>pontos <span class="blank _4"> </span>distintos <span class="blank _4"> </span>determinam <span class="blank _4"> </span>uma </div><div class="t m0 x9 h5 y9b ff2 fs3 fc0 sc0 ls2 wsa">única reta. Com base neste conteúdo responda: </div><div class="t m0 x9 h13 y9c ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y9d ff2 fs3 fc0 sc0 ls2 wsa">a) <span class="blank _c"> </span>Demostre <span class="blank _c"> </span>passo <span class="blank _c"> </span>a <span class="blank _c"> </span>passo <span class="blank _c"> </span>como <span class="blank _c"> </span>encontrar <span class="blank _c"> </span>e <span class="blank _c"> </span>escreva <span class="blank _c"> </span>a <span class="blank _c"> </span>equação <span class="blank _c"> </span>vetorial <span class="blank _c"> </span>da <span class="blank _c"> </span>reta <span class="blank _c"> </span>r <span class="blank _c"> </span>que<span class="blank _0"></span> </div><div class="t m0 x9 h5 y9e ff2 fs3 fc0 sc0 ls2 wsa">passa pelos pontos A = (5, -4, 2) e B = (3, 1, 6). </div><div class="t m0 x9 h13 y9f ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 ya0 ff1 fs3 fc0 sc0 ls2 wsa">Primeiro se determina um ponto como referência: A ou B. </div><div class="t m0 x9 h13 ya1 ff1 fs3 fc0 sc0 ls2 wsa">Ao escolher um ponto, temos o vetor diretor que depende do ponto escolhido. </div><div class="t m0 x9 h17 ya2 ff1 fs3 fc0 sc0 ls2 wsa">Ou seja, se escolher A, o vetor diretor<span class="ff5"> </span><span class="ws0">v</span><span class="ff5"> será: v <span class="ff6 ls10">\uf03d</span> <span class="ls15 wse">AB</span>. </span></div><div class="t m0 x9 h17 ya3 ff1 fs3 fc0 sc0 ls2 wsa">Agora, se o ponto escolhido for o B, o vetor diretor<span class="ff5"> </span><span class="ls15">v </span>será: v <span class="ff6 ls10">\uf03d</span><span class="lsc"> <span class="lse wsd">BA</span></span><span class="ff5">. </span></div><div class="t m0 x9 h17 ya4 ff1 fs3 fc0 sc0 ls2 wsa">Para este caso, trabalharemos com o ponto A.<span class="ff5"> </span></div><div class="t m0 x9 h13 ya5 ff1 fs3 fc0 sc0 ls2 wsa">O vetor diretor v <span class="ff6 ls10">\uf03d</span> AB <span class="ff6 ls10">\uf03d</span> <span class="lse">B <span class="ff6 ls10">\uf02d</span><span class="lsc"> <span class="ls10">A </span></span></span><span class="ff6 wsf">\uf03d</span> (<span class="ff6 ls10">\uf02d</span><span class="lsd wsc">2,</span><span class="lsc"> <span class="lsd wsc">5,</span> <span class="lsd wsc">4)<span class="blank _0"></span><span class="ls2 wsa"> </span></span></span></div><div class="t m0 x9 h13 ya6 ff1 fs3 fc0 sc0 ls2 wsa">A equação vetorial será: </div><div class="t m0 x9 h17 ya7 ff1 fs3 fc0 sc0 ls2 wsa">r :(x, y, z) <span class="ff6 wsf">\uf03d</span> (5, <span class="ff6 wsf">\uf02d</span><span class="lsd wsc">4,</span> 2) <span class="ff6 ls10">\uf02b</span><span class="ff5"> <span class="ff6 ls11">\uf06c</span><span class="ls16 ws10">.(<span class="ff6 ls10">\uf02d</span></span>2, 5, 4), <span class="ff6 ls11">\uf06c</span><span class="ls12"> </span><span class="ff6 wsf">\uf0ce</span> R</span> </div><div class="t m0 x9 h13 ya8 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 ya9 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 yaa ff2 fs3 fc0 sc0 lsd wsc">b)<span class="ls2 wsa"> Demonstre passo a passo como encontr<span class="blank _1"> </span>ar e escreva as equações paramétricas da reta </span></div><div class="t m0 x9 h5 yab ff2 fs3 fc0 sc0 ls2 wsa">r que passa pelos pontos A = (5, -4, 2) e B = (3, 1, 6). </div><div class="t m0 x9 h5 yac ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h13 yad ff1 fs3 fc0 sc0 ls2 wsa">Equações Paramétricas da Reta r: </div><div class="t m0 x9 h13 yae ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h4 yaf ff1 fs2 fc0 sc0 ls2 wsa">Primeiro determin<span class="blank _0"></span>e um ponto como refe<span class="blank _0"></span>rência: A <span class="blank _0"></span>ou B. </div><div class="t m0 x9 h4 yb0 ff1 fs2 fc0 sc0 ls2 wsa">Ao escolher um pont<span class="blank _0"></span>o, temos <span class="blank _0"></span>o vetor diretor<span class="blank _0"></span> que depende do p<span class="blank _0"></span>onto escolhido. </div><div class="t m0 x9 h4 yb1 ff1 fs2 fc0 sc0 ls2 wsa">Ou seja, se escolher A,<span class="blank _0"></span> o vetor diretor<span class="blank _0"></span> v será: v <span class="ff6 ls13">\uf03d</span><span class="ls14"> <span class="ls17 ws11">AB</span></span>.<span class="blank _0"></span> </div><div class="t m0 x9 h4 yb2 ff1 fs2 fc0 sc0 ls2 wsa">Agora, se o ponto <span class="blank _0"></span>escolhido for <span class="blank _0"></span>o B, o vetor diret<span class="blank _0"></span>or v será: v <span class="ff6 ls13">\uf03d</span><span class="ls14"> <span class="ls18 ws12">BA</span></span> </div><div class="t m0 x9 h4 yb3 ff1 fs2 fc0 sc0 ls2 wsa">Para este caso, tr<span class="blank _0"></span>abalharemos c<span class="blank _0"></span>om o ponto A. </div><div class="t m0 x9 h13 yb4 ff1 fs2 fc0 sc0 ls2 wsa">O vetor diretor <span class="blank _0"></span>v <span class="ff6 ls13">\uf03d</span> AB <span class="ff6 ls13">\uf03d</span> <span class="ls18">B <span class="blank _0"></span><span class="ff6 ls13">\uf02d<span class="ff1 ls14"> <span class="ls17">A </span></span>\uf03d<span class="ff1 ls2"> (<span class="ff6 ws13">\uf02d</span><span class="ls6 ws14">2,<span class="blank _0"></span><span class="ls2 wsa"> <span class="ls6 ws14">5,</span><span class="ls14"> <span class="ls19 ws15">4)</span></span><span class="fs3"> </span></span></span></span></span></span></div><div class="t m0 x9 h13 yb5 ff1 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h4 yb6 ff1 fs2 fc0 sc0 ls2 wsa">Equações para<span class="blank _0"></span>métricas: </div><div class="t m0 x9 h4 yb7 ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x10 h4 yb8 ff1 fs2 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y64 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y65 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y8f ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y67 ff2 fs3 fc0 sc0 ls2 wsa"> </div><div class="t m0 x9 h5 y68 ff2 fs3 fc0 sc0 ls2 wsa"> </div></div><div class="t m0 x2 h4 yb9 ff1 fs2 fc0 sc0 ls2 wsa"> </div><a class="l"><div class="d m1" style="border-style:none;position:absolute;left:267.610000px;bottom:682.630000px;width:127.880000px;height:14.650000px;background-color:rgba(255,255,255,0.000001);"></div></a></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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