Vektorlar nazariyasiga doir mashqlar. Tekislikdagi to‘g‘ri chiziq. Vektorlar ustida amallar

Vektorlar ustida amallar
Quyidagi masalalarda ABCD piramida uchlarining koordinatalari berilgan.

5. 
   , va vektorlar dekart bazislari i, j, k vektorlar orqali yozilsin va ularning uzunliklari topilsin.
   
6. 
   va vektorlar orasidagi burchak topilsin.
   
7. 
   ABC yoqning yuzi topilsin.
   
8. 
   ABCD piramidaning qajmi topilsin.
   

1. A (4; -2;5), B (8; 2; 3), C (6; 9; -5), D(4; 0; 6)

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