3.7. Компланарность векторов
Даны
точки А(
),
В(
),
C(
)
и D(
).
Являются ли векторы
,
,
компланарными? Выяснить, является ли
тройка векторов
,
,
правой, если векторы некомпланарны?
Вычислить направляющие косинусы вектора
.
Таблица 3.7 – Исходные данные
№ вар. |
А( ) |
В( ) |
C( ) |
D( ) |
1 |
2 |
3 |
4 |
5 |
1 |
(1; 2; 0) |
(1; -1; 2) |
(0; 1; -1) |
(-3; 0; 1) |
2 |
(1; 0; 2) |
(1; 2; -1) |
(2; -2; 1) |
(2; 1; 0) |
3 |
(1; 2; -3) |
(1; 0; 1) |
(-2; -1; 6) |
(0; -5; -4) |
4 |
(3; 10;-1) |
(-2; 3; -5) |
(-6; 0; -3) |
(1; -1; 2) |
5 |
(-1; 2; 4) |
(-1; -2; -4) |
(3; 0; -1) |
(7; -3; 1) |
6 |
(0; -3; 1) |
(-4; 1; 2) |
(2; -1; 5) |
(3; 1; -4) |
7 |
(1; 3; 0) |
(4; -1; 2) |
(3; 0; 1) |
(-4; 3; 5) |
8 |
(-2; -1; -1) |
(0; 3; 2) |
(3; 1; -4) |
(-4; 7; 3) |
9 |
(-3; -5; 6) |
(2; 1; -4) |
(0; -3; -1) |
(-5; 2; -8) |
10 |
(2; -4; -3) |
(5; -6; 0) |
(-1; 3; -3) |
(-10; -8; 7) |
11 |
(1; 3; 6) |
(2; 2; 1) |
(-1; 0; 1) |
(-4; 6; -3) |
12 |
(-4; 2; 6) |
(2; -3; 0) |
(-10; 5; 8) |
(-5; 2; -4) |
13 |
(7; 2; 4) |
(7; -1; -2) |
(3; 3; 1) |
(-4; 2; 1) |
14 |
(2; 1; 4) |
(-1; 5; -2) |
(-7; -3; 2) |
(-6; -3; 6) |
15 |
(-1; -5; 2) |
(-6; 0; -3) |
(3; 6; -3) |
(-10; 6; 7) |
16 |
(0; -1; -1) |
(-2; 3; 5) |
(1; -5; -9) |
(-1; -6; 3) |
17 |
(5; 2; 0) |
(2; 5; 0) |
(1; 2; 4) |
(-1; 1; 1) |
18 |
(2; -1; -2) |
(1; 2; 1) |
(5; 0; -6) |
(-10; 9; -7) |
19 |
(-2; 0; -4) |
(-1; 7; 1) |
(4; -8; -4) |
(1; -4; 6) |
20 |
(14; 4; 5) |
(-5; -3; 2) |
(-2; -6; -3) |
(-2; 2; -1) |
21 |
(1; 2; 0) |
(3; 0; -3) |
(5; 2; 6) |
(8; 4; -9) |
22 |
(2; -1; 2) |
(1; 2; -1) |
(3; 2; 1) |
(-4; 2; 5) |
23 |
(1; 1; 2) |
(-1; 1; 3) |
(2; -2; 4) |
(-1; 0 -2) |
24 |
(2; 3; 1) |
(4; 1; -2) |
(6; 3; 7) |
(7; 5; -3) |
25 |
(1; 1; -1) |
(2; 3; 1) |
(3; 2; 1) |
(5; 9; -8) |
26 |
(1; 5; -7) |
(-3; 6; 3) |
(-2; 7; 3) |
(-4; 8; -12) |
27 |
(-3; 4; -7) |
(1; 5; -4) |
(-5; -2; 0) |
(2; 5; 4) |
28 |
(-1; 2; -3) |
(4; -1; 0) |
(2; 1; -2) |
(3; 4; 5) |
29 |
(4; -1; 3) |
(-2; 1; 0) |
(0; -5; 1) |
(3; 2; -6) |
30 |
(1; -1; 1) |
(-2; 0; 3) |
(2; 1; -1) |
(2; -2; -4) |