Chapter 10 9x2 x2 x2 2 x 3 x center 1 3 1 3 1 9 2

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Unformatted text preview: 2, 2 1k 49. (a) v 0 3i 3i 3k − 3, 0, 3 5 4 3 2 1 1 2 −3 3 3j 3, 0, 3 3 0k (b) − 2, 2, 2 z 3 4 y 51. 4 1, 3, 1 1, 6 2, 6 1 1, 0 1 1, 36 1, 6 38 1 , 38 1 , 38 3k 6 38 53. 5 1, 0, 4 ,3 1 3, 0 1 1 , 0, 2 1 1 2 1 2 1, 0, 1 Unit vector: 1, 6 38 3 k 2j Unit vector: 55. (b) v 3 4i 1i j 4 57. q1, q2, q3 Q 3, 1, 8 0, 6, 2 3, 5, 6 4, 1, 1 (a) and (c). z 5 4 3 (3, 3, 4) (− 1, 2, 3) (0, 0, 0) 2 −2 v 2 4 y (4, 1, 1) 2 4 x 59. (a) 2v 2, 4, 4 z 5 4 3 2 −2 1 2 3 1 2 y (b) v 1, z 3 2 2, 2 −2 −3 2, 4, 4 −3 − 1, − 2, − 2 2 3 x −2 1 −2 −3 2 3 4 x —CONTINUED— Section 10.2 59. —CONTINUED— (c) 3 2 Space Coordinates and Vectors in Space 235 v 3 2, 3, 3 z (d) 0v 0, 0, 0 z 3 3 2 −3 −2 2 3 x −2 −3 3 , 2 2 −2 −3 3, 3 y −3 −2 1 2 3 1 0, 0, 0 −1 −2 −3 1 2 3 y 1 −2 −3 x 61. z 63. z 65. 2z 2z1 2z2 2z3 z 69. z u 2u 3u 3 6 9 7 2, v 4v 1, 2, 3 w 2, 2, 2, 4, 6 1 8, 8, 4 1, 0, 4 4, 0, 4 4 6, 12, 6 67. (a) and (b) are parallel since 6, 2 and 2, 4 , 130 3, 2, 5 . 3 3 4, 10 2 3, 2, 5 2 z1, z2, z3 4 ⇒ z1 0 ⇒ z2 4 ⇒ z3 7 2 3 1, 2, 3 4, 0, 3 5 2 3, 5 2 4j 2k 6i 8j 4k 2z. 71. P 0, 2, \ 3i 5 , Q 3, 4, 4 , R 2, 2, 1 3, 6, 9 2, 4, 6 3 2 (a) is parallel since PQ \ PR 3, 6, 9 2, 4, 6 \ \ Therefore, PQ and PR are parallel. The points are collinear. 73. P 1, 2, 4 , Q 2, 5, 0 , R 0, 1, 5 \ 75. A 2, 9, 1 , B 3, 11, 4 , C 0, 10, 2 , D 1, 12, 5 \ PQ \ 1, 3, 1, \ 4 1, 1 \ AB \ 1, 2, 3 1, 2, 3 2, 1, 1 2, 1, 1 \ \ \ \ PR CD \ Since PQ and PR are not parallel, the points are not collinear. AC \ BD Since AB CD and AC BD , the given points form the vertices of a parallelogram. 77. v 0 79. v v 83. u u (a) (b) u u u u 2, 4 1 2, 3 1, 2 1 4 1, 2 1 2, 3 1, 2 3 (a) (b) 85. u u u u u u 1, 1 2, 4 3 9 5 4 25 5 5 38 14 81. v v 0, 3, 0 5 9 25 34 3, 2, 9 87. Programs will vary. 1 3, 2, 38 1 3, 2, 38 236 Chapter 10 Vectors and the Geometry of Space u u 1 1 , 2 2 89. cv cv 9c 2 2c, 2c, 4c 2 25 ± c 4c 2 c2 5 91. v 10 10 0, 0, 10 10 , 2 2 c 5 3 32 21 , , 23 3 3 1 2 97. v 2 3v 93. v 3u 2u 1, 1, 95. v 2 cos ± 30 j 3j ...
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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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