Respostas dos Exercícios CVGA.

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Universidade Veiga deAlmeida
Professora: Adriana Nogueira
Curso: Ba´sico das engenharias
Disciplina: Ca´lculo Vetorial e Geometria Anal´ıtica
Respostas da 1a Lista de exerc´ıcios
Exerc´ıcio 2:
(a) −→p = −9−→i + 7−→j
(b) −→q = −22−→i + 7−→j
(c) −→r = 9−→i −−→j
(d) −→s = 2−→i + 7−→j
Exerc´ıcio 3:
(a) −→r = (13
3
, 0)
(b) −→r = (−60,−4)
Exerc´ıcio 4: a = 4 e b = −3
Exerc´ıcio 5:
(a) −→u = (−4,−1) (b) −→v = (2,−7) (c) −→w = (−3, 7)
Exerc´ıcio 6: B = (2,−3)
Exerc´ıcio 7: O quadrila´tero e´ um paralelogramo.
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Exerc´ıcio 8:
(a) |−−→AB| = 3√2 e |−−→BC| = 5
(b) d(A,C) = 1
(c) M = (−12 , 72)
Exerc´ıcio 9:
(a) −→v = (
√
26
26 ,
5
√
26
26 )
(b) −→v = (−
√
10
10 ,
3
√
10
10 )
Exerc´ıcio 10:
(a) |−→u | = √2, |−→v | = √13, |−→w | = √5
(b) |2−→u −−→v | = √41
(c) |−→u + 3−→v | = √89
Exerc´ıcio 11:
(a) −→v = (6, 15)
(b) −→v = (−10
√
29
29 ,
−25√29
29 )
(c) −→v = (−16
√
29
29 ,
−40√29
29 )
Exerc´ıcio 12: a = 2
√
6
5 e a =
−2√6
5
Exerc´ıcio 13: a = 117
Exerc´ıcio 14: a = 2
√
10 e a = −2√10
Exerc´ıcio 15: −→v = 6−→i
2