Задача 6

 

Средствами векторной алгебры найти:

1) объем пирамиды ;

2) длину ребра ;

3) площадь грани ;

4) угол между ребрами и .

Даны координаты вершин пирамиды:

 

1.	(1, 1, 1), (-1, 2, 4), (2, 0, 6), (-2, 5, -1)
2.	(0, 5, 0), (2, 3, -4), (0, 0, -6), (-3, 1, -1)
3.	(0, 0, 6), (4, 0, -4), (1, 3, -1), (4, -1, -3)
4.	(-5, 6, -1), (6, -5, 2), (6, 5, 1), (0, 0, 2)
5.	(2, -5, 3), (3, 2, -5), (5, -3, -2), (-5, 3, 2)
6.	(6, 0, 4), (0, 6, 4), (4, 6, 0), (0, -6, 4)
7.	(3, 2, 4), (2, 4, 3), (4, 3, -2), (-2, -4, -3)
8.	(6, 3, 5), (5, -6, 3), (3, 5, 6), (-6, -1, 2)
9.	(5, -2, -1), (4, 0, 0), (2, 5, 1), (1, 2, 5)
10.	(4, 2, 5), (3, 0, 4), (0, 0, 3), (5, -2, -4)
11.	(4, 2, -5), (3, 0, 4), (0, 2, 3), (5, 2, -4)
12.	(4, 4, 10), (7, 10, 2), (2, 8, 4), (9, 6, 9)
13.	(4, 6, 5), (6, 9, 4), (2, 10, 10), (7, 5, 9)
14.	(3, 5, 4), (8, 7, 4), (5, 10, 4), (4, 7, 8)
15.	(10, 6, 6), (-2, 8, 4), (6, 8, 9), (7, 10, 3)
16.	(1, 8, 2), (5, 2, 6), (5, 7, 4), (4, 10, 9)
17.	(6, 6, 5), (4, 9, 5), (4, 6, 11), (6, 9, 3)
18.	(7, 2, 2), (5, 7, 7), (5, 3, 1), (2, 3, 7)
19.	(8, 6, 4), (10, 5, 5), (5, 6, 8), (8, 10, 7)
20.	(7, 7, 3), (6, 5, 8), (3, 5, 8), (8, 4, 1)
21.	(4, 0, 0), (-2, 1, 2), (1, 3, 2), (3, 2, 7)
22.	(-2, 1, 2), (4, 0, 0), (3, 2, 7), (1, 3, 2)
23.	(1, 3, 2), (3, 2, 7), (4, 0, 0), (-2, 1, 2)
24.	(3, 2, 7), (1, 3, 2), (-2, 1, 2), (4, 0, 0)
25.	(3, 1, -2), (1, -2, 1), (-2, 1, 0), (2, 2, 5)
26.	(1, -2, 1), (3, 1, -2), (2, 2, 5), (-2, 1, 0)
27.	(-2, 1, 0), (2, 2, 5), (3, 1, 2), (1, -2, 1)
28.	(2, 2, 5), (-2, 1, 0), (1, -2, 1), (3, 1, 2)
29.	(1, -1, 6), (4, 5, -2), (-1, 3, 0), (1, -1, 5)
30.	(6, 1, 5), (-1, 3, 0), (4, 5, -2), (1, -1, 6)