Векторная алгебра. Попов В.А - 6 стр.

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8
26.
a
{2; –7; 5}, b {–1; 2; –6},
с
{3; 2; –4}.
27. a {3; 1; –3}, b {–2; 4; 1},
с
{1; –2; 5}.
28. a {4; 2; 3}, b {–3; 1; –8},
с
{2; –4; 5}.
29. a {0; 2; –3}, b {4; –3; –2},
с
{–5; –4; 0}.
30. a {1; 3; 6}, b {–3; 4; –5},
с
{1; –7; 2}.
3. Доказать, что векторы a , b и
с
образуют базис, и найти координаты вектора d в этом базисе.
1. a {2; 1; 1}, b {–1; 3; –2},
с
{3; –1; 2}, d {–4; 11; –7}.
2. a {3; 3; 2}, b {–2; 4; –1},
с
{4; –2; –1}, d {12; 6; –9}.
3. a {2; 2; 3}, b {1; 3; 2},
с
{3; 1; 1}, d {7; 1; 6}.
4. a {8; 1; 4}, b {3; 1; 1},
с
{–6; –1; –3}, d {–4; 2; –5}.
5. a {2; 3; 3}, b {–1; 4; –2},
с
{–1; –2; 4}, d {4; 11; 11}.
6. a {3; 2; 2}, b {2; 3; 1},
с
{1; 1; 3}, d {5; 1; 1}.
7. a {1; 2; 4}, b {1; –1; 1},
с
{2; 2; 4}, d {–1; –4; –2}.
8. a {1; 2; 4}, b {5; –3; 1},
с
{–4; 1; –3}, d {–5; 2; –4}.
9. a {2; 3; 1}, b {–1; 2; –2},
с
{1; 2; 1}, d {2; –2; 1}.
10. a {1; 2; 1}, b {3; –1; 2},
с
{4; –1; 3}, d {6; 1; 5}.
11. a {2; 1; 1}, b {–4; –5; –1},
с
{1; 3; 1}, d {3; –1; 1}.
12. a {1; 2; 1}, b {–1; 1; 1},
с
{1; 1; 2}, d {6; 3; 5}.
13. a {2; –1; 3}, b {–1; 3; 2},
с
{1; –1; 1}, d {4; –3; 3}.
14. a {3; 1; 1}, b {1; 1; –2},
с
{–2; 1; 3}, d {–2; 0; –3}.
15. a {1; –2; 1}, b {2; –3; 5},
с
{–1; 2; 1}, d {1; 0; –5}.
16. a {2; 1; –2}, b {–3; –5; –1},
с
{1; –2; 3}, d {–3; 6; –9}.
17. a {3; 1; 1}, b {1; 2; 4},
с
{1; 2; –1}, d {4; 3; –2}.
18. a {4; 1; –1}, b {–1; 3; 2},
с
{–1; 3; –1}, d {0; –4; 5}.
19. a {2; 5; –1}, b {–1; 3; –2},
с
{0; –6; 3}, d {7; –5; 7}.
20. a {3; 1; 2}, b {–1; 2; –1},
с
{1; –1; 3}, d {12; 12; 9}.
21. a {1; 1; 3}, b {3; –1; –2},
с
{–2; 4; –1}, d {–4; 4; –9}.
22. a {2; 2; 3}, b {1; 0; 1},
с
{1; 1; 2}, d {6; 13; 8}.
23. a {3; 2; 1}, b {–2; 3; –2},
с
{–5; –4; 3}, d {5; 12; –1}.
24. a {2; 4; 1}, b {–1; 1; 1},
с
{2; 4; 2}, d {0; 6; –4}.
25. a {2; 3; 1}, b {–1; 4; 5},
с
{–3; 2; 1}, d {1; 0; –3}.
26. a {–3; 3; 1}, b {5; 1; –4},
с
{6; 1; –2}, d {–8; –4; –9}.
27. a {2; 2; 3}, b {3; 1; 2},
с
{1; 3; 1}, d {4; 0; 1}.
28. a {1; 2; 3}, b {5; 4; –1},
с
{–1; –3; –3}, d {3; 2; 7}.
29. a {2; 3; 5}, b {–1; –1; 2}, c {5; 5; 13}, d {4; 0; 2}.
30. a {1; 2; 1}, b {–2; –1; 0}, c {–1; 0; 1}, d {–2; –1; –2}.
4. Вершины пирамиды находятся в точках
A
,
B
,
C
и
D.
Вычислите:
а) площадь указанной грани; б) площадь сечения, проходящего через середину ребра l и две вершины пирамиды; в)
объём пирамиды
ABCD
.
1.
A
(3; 4; 5),
B
(1; 2; 1),
C
(–2; –3; 6),
D
(3; –6; –3);
а)
ACD
; б)
l
=
AB
,
C
и
D
.
2.
A
(–7; –5; 6),
B
(–2; 5; –3),
C
(3; –2; 4),
D
(1; 2; 2);
а)
BCD
; б)
l
=
CD
,
A
и
B
.
3.
A
(–1; 4; 5),
B
(1; 2; 1),
C
(–2; –1; 6),
D
(–1; –6; –1);
а)
ABC
; б)
l
=
AB
,
C
и
D
.
4.
A
(–2; 4; 5),
B
(2; 2; 2),
C
(–2; –2; 6),
D
(–2; –6; –2);
а)
BCD
; б)
l
=
BD
,
A
и
C
.

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