A u b v c v v u v ijk 234 372 u v 22 0 22 16 16

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Unformatted text preview: v u v 0⇒u 2 2 0⇒v z z v v u 4 6 y x 4 3 u 4 6 y 21. u v u u u v 4, 3.5, 7 1, 8, 4 70, 23, 57 2 46 , 24,965 57 24,965 23. u v u u u 1 i 2 v v v 3i 2j 3 j 4 71 , 20 5k 1 k 10 11 5 , 54 71 , 20 11 5 , 54 44 , 7602 25 7602 v v 140 , 24,965 20 7602 71 , 7602 25. Programs will vary. 27. u v u A j j v u k ijk 010 011 v i 1 i 29. u v u A v u 3, 2, 1, 2, 3 i 3 1 v j 2 2 8, k 1 3 1 8, 10, 4 10, 4 180 65 31. A 1, 1, 1, , B 2, 3, 4 , C 6, 5, 2 , D 7, 7, 5 \ \ \ 33. A 0, 0, 0 , B 1, 2, 3 , C \ \ 3, 0, 0 3, 0, 0 AB BD \ 1, 2, 3 , AC 5, 4, 1 \ \ \ \ 5, 4, 1 , CD \ \ 1, 2, 3 , AB \ 1, 2, 3 , AC \ Since AB CD and AC BD , the figure is a parallelogram. AB and AC are adjacent sides and \ \ AB AC 1 AB 2 i 1 3 \ \ j 2 0 1 2 k 3 0 117 9j 3 2 6k AB A AC \ ijk 123 541 \ 10i 2 83 14j 6k. A AC 13 AB AC 332 Section 10.4 35. A 2, \ The Cross Product of Two Vectors in Space 20k \ 243 7, 3 , B 1, 5, 8 , C 4, 6, \ 1 4 113, 2, 63 37. F PQ \ AB \ \ 3, 12, 5 , AC AC 1 AB 2 i j 3 12 2 13 \ \ 2, 13, k 5 4 1 2 AB PQ \ 1 cos 40 j sin 40 k 2 i j k F 0 cos 40 2 sin 40 2 0 0 20 F z 10 cos 40 i Area AC 16,742 PQ 10 cos 40 7.66 ft lb PQ 1 ft 2 40° F y x \ 39. (a) OA F \ 3 k 2 60 sin j i 0 0 j 0 60 sin cos k k 32 60 cos 90 sin i OA 1.5 ft z 100 F θ OA \ F F y 0 0 180 OA (b) When (c) Let T dT d 90 sin \ x 45 : OA 90 sin . 90 cos F 90 2 2 45 2 63.64. 0 when 90 . 90 the pipe wrench is horizontal. 2 0 0 0 3 0 1 0 1 1 0 1 w 1 1 0 2 0 1 1 This is what we expected. When 1 0 0 0 1 0 0 0 1 41. u v w 1 43. u v w 6 45. u V v u w v 2 47. u v w u V 49. u v v 3, 0, 0 0, 5, 1 2, 0, 5 w v 3 0 2 w 0 5 0 0 1 5 75 v1, v2, v3 u 2v3 u 3v2 i u 1v3 u 3v1 j u 1v2 u 2v1 k 75 u u1, u2, u3 51. The magnitude of the cross product will increase by a factor of 4. 55. True 53. If the vectors are ordered pairs, then the cross product does not exist. False. 244 57. u u Chapter 10 u1, u2, u3 , v v w v1 Vectors and the Geometry of Space v1, v2, v3 , w i u1 w1 v2 w3 u3v2 i u3w1 j u w u2 v3 u2v3 u1w3 u v j u2 w2 u3 v2 u1v3 v3 w1, w2, w3 k u3 w3 u1 v3 u1...
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This note was uploaded on 05/18/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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