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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 2a Lista de exerc´ıcios
Exerc´ıcio 2:
(a) −→r = (7, 3,−19)
(b) −→r = (32,−32, 10)
(c) −→r = (7,−3, 1)
(d) −→r = (6, 3,−2).
Exerc´ıcio 3:
(a) −−→AB = (2,−4,−1), −−→CB = (2,−3, 6) e −→AC = (0,−1,−7);
(b) |−−→AB| = √21, |−−→BC| = 7;
(c) d(A,C) = 5
√
2;
(d) O ponto me´dio entre A e B e´ M = (2, 0, 112 );
(e) O ponto me´dio entre A e C e´ M = (1, 32 ,
5
2).
Exerc´ıcio 4:
(a)−→v = (
√
30
30 ,
√
30
6 ,
√
30
15 ); (b)
−→v = (−
√
10
10 ,
3
√
10
10 , 0); (c)
−→v = (
√
38
38 ,
√
38
38 ,
3
√
38
19 );
Exerc´ıcio 5: A = (3, 7, 3).
Exerc´ıcio 6: (a) |−→u | = √14; (b) |−→−→u | = √26; (c) |−→u | = √11.
1
Exerc´ıcio 7: (a) −→v = (5, 15, 10); (b) −→v = (−5
√
14
14 ,
−15√14
14 ,
−5√14
7 ).
Exerc´ıcio 8:
(a) 2 (b) 7 (c) 1 (d)
√
53 (e) 5
√
2 (f)
√
5.
Exerc´ıcio 9: −→u , −→v e −→t sa˜o paralelos.
Exerc´ıcio 10: S = {−
√
23
6 ,
√
23
6 }.
Exerc´ıcio 11: C = (3,−3,−3) e D = (0,−4,−1).
Exerc´ıcio 12: P = (
√
15− 1, 0, 0).
Exerc´ıcio 13: D = (6, −43 ,
8
3).
Exerc´ıcio 14: a =
√
17 ou a = −√17.
Exerc´ıcio 15: a = 72 , b =
−5
2 , c = −17
2