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9.9. : | a | = 3, | b | = 4, Ð(a, b) = 2p/3. (a + b)2.

9.10. : | a | = 3, | b | = 5. , a

(a + a b) (a a b) .

9.11. a b, a = 3 m + 2 n, b = m n, m n - , | m | = 2, | n | = 1.

9.12. : | a | = 3, | b | = | c | = 2. a b , c , π/3. (2 a b) ( b).

9.13. a = (4, 2, 4) b = (6, 3, 2). :

a) a b; ) (2 a 3 b)(a + 2 b); ) (a b)2; ) |2 a b |; ) a b; ) ba;

) a;. ) a + b (a 2 b); ) cos (a, b).

9.14. , A ( 3, 5, 6), B (1, 5, 7),

C (8, 3, 1), D (4, 7, 2) .

9.15. cos j, j - AC BD , : A (2, 1, 3), B (5, 2, 1), C ( 3, 3, 3).


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9.16. : | a | = 3, | b | = 4, j =Ð(a, b) = 120.

c = 3 a + 2 b.

9.17. e 1, e 2, e 3,

e 1 + e 2 + e 3 = o. e 1 e 2 + e 2 e 3 + e 3 e 1.

9.18. a b, a = 3 m + 2 n, b = 2 m + n, m n - , | m | = 2, | n | = 1.

9.19. : | a | = 3, | b | = | c | = 2. a b , c , π/3. (2 a + 3 b) ( b).

9.20. , a = 2 i + j b = j + 2 k..

9.21. l b = l i 5 j + 3 k

c = i + 2 j l k ?

9.22. a b, , m = a + 2 b n = 5 a 4 b .

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9.1. a) 9; ) 61. 9.2. p/3. 9.3. 1. 9.4. 5. 9.5. 5. 9.6. cosj = .

9.7. . 9.8. ; . 9.9. 13. 9.10. a = 3/5. 9.11. 10. 9.12. 7.

9.13. a) 22; ) 200; ) 41; ) ; ) 11/3; ) 22/7;

) cosa = 2/3, cosb = 1/3, cosg = 2/3; ) 84/ ; ) 11/21.

9.15. cosj = 43/25 . 9.16. . 9.17. 1,5. 9.18. 26. 9.19. 0.

9.20. p/2. 9.21. 5. 9.22. p/3.

 

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