Задача № 6.
Определить
компланарны ли вектора
,
и
.
|
№ п/п |
|
|
|
|
6.1 |
(2, 3,1) |
(-1, 0, -1) |
(2, 2, 2) |
|
6.2 |
(3, 2, 1) |
(2, 3, 4) |
(3, 1, -1) |
|
6.3 |
(1, 5, 2) |
(-1, 1, -1) |
(1, 1, 1) |
|
6.4 |
(1, -1, -3) |
(3, 2, 1) |
(2, 3, 4) |
|
6.5 |
(3, 3, 1) |
(1, -2, 1) |
(1, 1, 1) |
|
6.6 |
(3, 1, -1) |
(-2, -1, 0) |
(5, 2, -1) |
|
6.7 |
(4, 3, 1) |
(1, -2, 1) |
(2, 2, 2) |
|
6.8 |
(4, 3, 1) |
(6, 7, 4) |
(2, 0, -1) |
|
6.9 |
(3, 2, 1) |
(1, -3, -7) |
(1, 2, 3) |
|
6.10 |
(3, 7, 2) |
(-2, 0, -1) |
(2, 2, 1) |
|
6.11 |
(1, -2, 6) |
(1, 0, 1) |
(2, -6, 17) |
|
6.12 |
(6, 3, 4) |
(-1, -2, -1) |
(2, 1, 2) |
|
6.13 |
(7, 3, 4) |
(-1, -2, -1) |
(4, 2, 4) |
|
6.14 |
(2, 3, 2) |
(4, 7 , 5) |
(2, 0, -1) |
|
6.15 |
(5, 3, 4) |
(-1, 0, -1) |
(4, 2, 4) |
|
6.16 |
(3, 10, 5) |
(-3, -2, -3) |
(2, 4, 3) |
|
6.17 |
(-2, -4, -3) |
(4, 3, 1) |
(6, 7, 4) |
|
6.18 |
(3, 1, -1) |
(1, 0, -1) |
(8, 3, -2) |
|
6.19 |
(4, 2, 2) |
(-3, -3, -3) |
(2, 1, 2) |
|
6.20 |
(4, 1, 2) |
(9, 2, 5) |
(1, 1, -1) |
|
6.21 |
(5, 3, 4) |
(4, 3, 3) |
(9, 5, 8) |
|
6.22 |
(3, 4, 2) |
(1, 1, 0) |
(8, 11, 6) |
|
6.23 |
(4, -1, -6) |
(1, -3, -7) |
(2, -1, -4) |
|
6.24 |
(3, 1, 0) |
(-5, -4, -5) |
(4, 2, 4) |
|
6.25 |
(3, 0, 3) |
(8, 1, 6) |
(1, 1, -1) |
|
6.26 |
(1, -1, 4) |
(1, 0, 3) |
(1, -3, 8) |
|
6.27 |
(6, 3, 4) |
(-1, -2, -1) |
(2, 1, 2) |
|
6.28 |
(4, 1, 1) |
(-9, -4, -9) |
(6, 2, 6) |
|
6.29 |
(-3, 3, 3) |
(-4, 7, 6) |
(3, 0, -1) |
|
6.30 |
(-7, 10, -5) |
(0, -2, -1) |
(-2, 4, -1) |
Задача № 7.
Вычислить объем
пирамиды с вершинами в точках
,
,
и
и ее высоту, опущенную из вершины
на грань
.
|
№ п/п |
|
|
|
|
|
7.1 |
(0, 1, 2) |
(2, 1, 7) |
(2, 7, 4) |
(0, 0, 4) |
|
7.2 |
(1, 2, 3) |
(2, 8, -4) |
(0, 5, 4) |
(2, 9, 4) |
|
7.3 |
(1, 1, 1) |
(2, 4, -2) |
(2, 0, 2) |
(0, 1, -1) |
|
7.4 |
(1, -1, 1) |
(0, 2, 3) |
(1, -1, 0) |
(0, 2, 2) |
|
7.5 |
(2, 1, 3) |
(4, -2, 0) |
(1, 3, -3) |
(7, 5, 2) |
|
7.6 |
(-2, 0, 4) |
(1, 3, -1) |
(4, -1, 3) |
(2, 7, 3) |
|
7.7 |
(1, 2, 3) |
(0, 0, 0) |
(1, 4, 3) |
(1, 8, -1) |
|
7.8 |
(-1, 2, 0) |
(1, 0, 3) |
(0, 2, 2) |
(1, 8, 3) |
|
7.9 |
(2, -1, 1) |
(3, 3, 2) |
(2, 1, 0) |
(4, 1, -3) |
|
7.10 |
(2, 1, -1) |
(-3, 1, 2) |
(0, 1, 2) |
(-1, 8, 3) |
|
7.11 |
(-2, 1, 1) |
(5, 5, 4) |
(3, 2, -1) |
(4, 1, 3) |
|
7.12 |
(0, 1, -1) |
(3, -1, 5) |
(1, 0, 4) |
(3, 5, 7) |
|
7.13 |
(1, 1, 2) |
(-1, 1, 3) |
(2, -2, 4) |
(-1, 0, -2) |
|
7.14 |
(2, 3, 1) |
(4, 1, -2) |
(6, 3, 7) |
(7, 5, -3) |
|
7.15 |
(1, 1, -1) |
(2, 3, 1) |
(3, 2, 1) |
(5, 9, -8) |
|
7.16 |
(1, 5, -7) |
(-3, 5, 3) |
(-2, 7, 3) |
(-4, 8, -12) |
|
7.17 |
(-3, 4, -7) |
(1, 5, -4) |
(-6, -2, 0) |
(2, 5, 4) |
|
7.18 |
(-1, 2, -3) |
(4, -1, 0) |
(2, 1, -2) |
(3, 4, 5) |
|
7.19 |
(4, -1, 3) |
(-2, 1, 0) |
(0, -5, 1) |
(3, 2, -6) |
|
7.20 |
(1, -1, 1) |
(-2, 0, 3) |
(2, 1, -1) |
(2, -2, -4) |
|
7.21 |
(1, 2, 0) |
(1, -1, 2) |
(0, 1, -1) |
(-3, 0, 1) |
|
7.22 |
(1, 0, 2) |
(1, 2, -1) |
(2, -2, 1) |
(2, 1, 0) |
|
7.23 |
(1, 2, -3) |
(1, 0, 1) |
(-2, -1, 6) |
(0, -5, -4) |
|
7.24 |
(3, 10, -1) |
(-2, 3, -5) |
(-6, 0, -3) |
(1, -1, 2) |
|
7.25 |
(-1, 2, 4) |
(-1, -2, -4) |
(3, 0, -1) |
(7, -3, 1) |
|
7.26 |
(0, -3, 1) |
(-4, 1, 2) |
(2, -1, 5) |
(3, 1, -4) |
|
7.27 |
(1, 3, 0) |
(4, -1, 2) |
(3, 0, 1) |
(-4, 3, 5) |
|
7.28 |
(-2, -1, -1) |
(0, 3, 2) |
(3, 1 , -4) |
(-4, 7, 3) |
|
7.29 |
(-3, -5, 6) |
(2, 1, -4) |
(0, -3, -1) |
(-5, 2, -8) |
|
7.30 |
(2, -4, -3) |
(5, 6, 0) |
(-1, 3, -3) |
(-10, -8, 7) |
