7.17. ABC : = a, = b, M - BC. a b.
7.18. l 2l a (l3 - 1) a, (a ¹ o), ?
7.19. x x 3 a (x 2 - x - 2) a, a ¹ o, ?
7.20. : | a | = 13, | b | = 19, | a + b | = 24. : | a - b |.
7.21. : a ^ b, | a | = 5, | b | = 12. : | a + b | | a - b |.
7.22. ABC: M - , = a, = b. a b.
7.23. ABCD: K M - BC CD, = a, = b. a b.
7.24. , l, m, n, a, b, c: l = a + 2 b, m = b +2 c, n = c. .
7
7.2. .
7.3. .
7.4. = , = , = , = .
7.5. ) -2; ) - 1; ) 1. 7.6. ) , ; ) c = m + n.
7.7. , 0 l - 2 m + n = 0.
7.13. ) ; ) ; ) .
7.14. ; l + m - n = 0. 7.16. l = m = 1. 7.17. .
7.18. (- ¥; 0)È(1; ¥). 7.19. (- ¥; - 1)È(0; 2). 7.20. 22. 7.21. 13; 13.
7.22. 3 a - b; 2 b - 3 a. 7.23. 2 b - 2 a. 7.24. .
8.
: ; ; ; .
1. | 8.1 - 8.3 | 8.10 - 8.12 | 8.19 - 8.21 |
2. . | 8.4 - 8.6 | 8.13 - 8.15 | 8.22 - 8.24 |
3. | 8.7 | 8.16 | 8.25 - 8.27 |
4. | 8.8, 8.9 | 8.17, 8.18 |
. a 0.
8.1. a = ( 1, 2, 0), b = (3, 1, 1), c = (2, 0, 1) d = a 2 b + c.
: a) | a | a 0 a; ) ;
) dx d; ) j d.
8.2. x, a = i 2 j 2 k, j | x | = 15.
8.3. a = (14, 22, 7).
8.4. :
) (1, 4) (2, 8); ) (2, 2, 3) (4, 4, 4); ) (3, 2), (6, 4) ( 12, 8);
) (4, 1, 2), (2, 1, 1) ( 2, 3, 1).
8.5. a = (2, 1), b = (1, 2), c = (4, 3). m = a + b + c a b.
8.6. , a = (1, 0, 0), b = (1, 1, 0), c = (1, 1, 1) . d = 2 i k (a, b, c) .
8.7. A ( 2, 6), B (2, 8)
|
|
M (2, 2). .
8.8. A (3, 1, 5), B (4, 2, 5), C ( 4, 0, 3). , A.
8.9. ,
C (2, 0, 2) D (5, 2, 0) .
8
8.10. a = 2 i + 3 j, b = 3 j 2 k, c = i + j k. :
a) ;
) a 0,5 b + c;
) a + b 2 c (i, j, k);
) j (a b).
8.11. x, , | x | = 2 .
8.12. a = (13, 6, 18)..
8.13. :
) (1, 4) (2, 5); ) (2, 2, 3) (6, 6, 9); ) (3, 2), (6, 4) ( 12, 8);
) (5, 2, 1), ( 1, 2, 3) (1, 1, 3).
8.14. a = (2, 1), b = (1, 2), c = (4, 3). m = a + b + c b c.
8.15. a = ( 1, 2), b = (2, 1) c = (0, 2). , (a, b) - . c (a, b).
8.16. A (3, 4, 7), B ( 5, 3, 2), C (1, 2, 3) ABCD. D, B.
8.17. M, A (1, 4, 7)
B (5, 6, 5).
8.18. A (3, 2) B (6, 4) . .