12 u meaningless explain a a b c c a b c e a b c 1

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Unformatted text preview: unit vector, find u v and u w. 12. 11. (b) a b c (d) a b c (f) a bc u v v w 2. Find the dot product of two vectors if their lengths are 6 1 3 and and the angle between them is u 4. w 3–10 |||| Find a b. 3. a 4, 4. a 1 2 1, b ,4 , 3, 6 b 8, ■ 3 5. a 5, 0, 2, b s, 2 s, 3s , b t, 7. a i 8. a 4j 9. a 10. ■ a ■ 3 k, 2j b 3 k, b 12, 4, ■ b 15, 10, b ■ ■ 1, 10 5i ■ jk jj ■ ki kk ■ ■ ■ ■ ■ 0. 1. drinks on a given day. He charges $2 for a hamburger, $1.50 for a hot dog, and $1 for a soft drink. If A a, b, c and P 2, 1.5, 1 , what is the meaning of the dot product A P ? 6k the angle between a and b is 15–20 |||| Find the angle between the vectors. (First find an exact expression and then approximate to the nearest degree.) 6 15. a the angle between a and b is 120° ■ ■ 14. A street vendor sells a hamburgers, b hot dogs, and c soft 9k 4j ■ ■ (b) Show that i i t, 5t 2i ■ 13. (a) Show that i j 3, 6. a ■ ■ ■ ■ ■ ■ 3, 4 , b 16. a s3 , 1 , 5, 12 b 0, 5 5E-13(pp 848-857) 1/18/06 11:18 AM Page 849 S ECTION 13.3 THE DOT PRODUCT 17. a 1, 2, 3 , 18. a 6, 19. a 4, 0, 3, 2 , b j 20. a b 2i k, b j 2, 1, i k, 2j b 37. a 1 38. a 2 2j 40. a k i 2i ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ ■ b k, b ■ b 3, 3, 4 i 3j j k, ■ 849 1, 1, 1 2, 2 , 1, 39. a 3k 3i 4, 2, 0 , ❙❙❙❙ b 6j ■ ■ i 2k ■ ■ ■ ■ ■ ■ ■ Find, correct to the nearest degree, the three angles of the triangle with the given vertices. 41. Show that the vector orth a b 21. A 1, 0 , 42. For the vectors in Exercise 36, find orth a b and illustrate by 21–22 |||| B 3, 6 , 22. D 0, 1, 1 , ■ ■ E ■ C 1, 4 2, 4, 3 , ■ ■ drawing the vectors a, b, proj a b, and orth a b. F 1, 2, ■ b proj a b is orthogonal to a. (It is called an orthogonal projection of b.) ■ 1 43. If a ■ ■ ■ ■ 3, 0, 1 , find a vector b such that comp a b 2. ■ 44. Suppose that a and b are nonzero vectors. 23–24 (a) Under what circumstances is comp a b comp b a? (b) Under what circumsta...
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