„ВЕКТОРНА АЛГЕБРА”
Задача 4Дано координати вершин піраміди ABCD. Потрібно:
1) записати вектори в системі орт;
2) знайти напрямні косинуси векторів ;
3) знайти проекцію вектора на вектор ;
4) знайти об’єм піраміди ABCD, та висоту, опущену із вершини D на грань ABC.
№ варіанта | А | В | С | D |
(3, 1, -2) | (4, -1, 0) | (14, 3, 8) | (11, 5, 6) | |
(0, 2, -10) | (1, 0, -8) | (11, 4, 0) | (8, 6, -2) | |
(-8, 3, -1) | (-7, 1, 1) | (3, 5, 9) | (0, 7, 7) | |
(-1, -2, -8) | (0, -4, -6) | (10, 0, 2) | (7, 2, 0) | |
(2, -1, -4) | (3, -3, -2) | (13, 1, 6) | (10, 3, 4) | |
(1, -4, 0) | (2, -6, 2) | (12, -2, 10) | (9, 0, 8) | |
(-4, 5, -5) | (-3, 3, -3) | (7, 7, 5) | (4, 9, 3) | |
(-5, 0, 1) | (-4, -2, 3) | (6, 2, 11) | (3, 4, 9) | |
(-2, -3, 2) | (-1, -5, 4) | (9, 1, 12) | (6, 1, 10) | |
(4, -2, 5) | (8, 2, 3) | (6, 9, -5) | (4, 0, 6) | |
(-3, 4, -3) | (-2, 2, -1) | (8, 6, 7) | (5, 8, 5) | |
(3, 3, -3) | (7, 7, -5) | (5, 14, -13) | (3, 5, -2) | |
(5, 0, 4) | (9, 4, 2) | (7, 11, -7) | (5, 2, 5) | |
(0, 4, 3) | (4, 8, 1) | (2, 15, -7) | (0, 6, 4) | |
(9, 3, 0) | (13, 7, 2) | (11, 14, -10) | (9, 5, 1) | |
(-2, 0, -2) | (2, 4, -4) | (0, 11, -12) | (-2, 2, -1) | |
(3, -2, 2) | (7, 2, 0) | (5, 9, -8) | (3, 0, 3) | |
(-4, 2, -1) | (0, 6, -3) | (-2, 13, -11) | (-4, 4, 0) | |
(0, -3, 5) | (4, 1, 3) | (2, 8, -6) | (0, -1, 6) | |
(-1, -1, -5) | (3, 5, -7) | (1, 12, -15) | (-1, 3, -4) | |
(3, 5, -1) | (7, 9, -3) | (5, 16, -11) | (3, 7, 10) | |
(-3, -6, 2) | (1, -2, 0) | (-1, 2, 8) | (-3, -4, 3) | |
(-1, 5, 2) | (3, 9, 0) | (1, 16, -8) | (-1, 7, 3) | |
(1, -4, 3) | (5, 0, -2) | (3, 7, -10) | (-1, -2, 1) | |
(-2, 2, 1) | (2, 6, -1) | (0, 13, -9) | (-2, 4, 2) | |
(5, -1, -4) | (9, 3, -6) | (7, 10, -14) | (5, 1, -3) | |
(0, 2, 0) | (4, 6, -2) | (2, 13, -10) | (0, 4, 1) | |
(0, -1, -1) | (-2, 3, 5) | (1, -5, -9) | (-1, -6, 3) | |
(2, -3, 1) | (6, 1, -1) | (4, 8, -9) | (2, -1, 2) | |
(2, 3, 1) | (4, 1, -2) | (6, 3, 7) | (7, 5, -3) |