Odd10

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Unformatted text preview: CHAPTER 10 Vectors and the Geometry of Space Section 10.1 Vectors in the Plane . . . . . . . . . . . . . . . . . . . . 227 Section 10.2 Space Coordinates and Vectors in Space . . . . . . . . . . 232 Section 10.3 The Dot Product of Two Vectors . . . . . . . . . . . . . . 238 Section 10.4 The Cross Product of Two Vectors in Space . . . . . . . . 241 Section 10.5 Lines and Planes in Space . . . . . . . . . . . . . . . . . 244 Section 10.6 Surfaces in Space . . . . . . . . . . . . . . . . . . . . . . 249 Section 10.7 Cylindrical and Spherical Coordinates . . . . . . . . . . . 252 Review Exercises . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256 Problem Solving . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 261 CHAPTER 10 Vectors and the Geometry of Space Section 10.1 Vectors in the Plane Solutions to Odd-Numbered Exercises 1. (a) v (b) 5 4 3 y 5 1, 3 1 4, 2 3. (a) v (b) 4 3, 2 y 2 7, 0 4 2 (− 7, 0) (4, 2) −8 −6 −4 v −2 −2 x 2 1 1 v x −4 2 3 4 5 5. u v u 5 1 v 3, 6 2 4 2, 4 2, 4 7. u v u 6 9 v 0, 3, 5 2 3 10 6, 6, 5 5 1 ,8 9. (b) v 5 1, 5 y 2 4, 3 (5, 5) 11. (b) v 6 10, 1 y 6 4 2 4, 3 (a) and (c). 4 (a) and (c). (10, 2) x 2 10 2 (4, 3) −4 2 v (1, 2) (6, −1) v x (− 4, − 3) 2 4 13. (b) v 6 6, 6 y 2 0, 4 15. (b) v 1 2 3 2, 3 4 3 y 1, 5 3 (a) and (c). 6 (a) and (c). (6, 6) 3 ( 1 , 3( 2 (−1, 5 ( 3 2 4 (0, 4) v (6, 2) x 2 4 6 v −2 −1 1 2 ( 3 , 4( 23 x 2 17. (a) 2v y 4, 6 (b) 3v 6, y 9 (2, 3) v x 4 6 (4, 6) 2v (2, 3) −8 −4 4 4 − 3v − 4 −8 2 v x 2 4 6 (− 6, − 9) —CONTINUED— 227 228 Chapter 10 Vectors and the Geometry of Space 17. —CONTINUED— (c) 7 2v y 12 7, 221 (d) 2 3 v y 4 3, 2 (7, 21 ( 2 3 (2, 3) v 8 7 v 2 4 2 ( 4 , 2( 3 2 v 3 x (2, 3) v 4 8 12 x 1 1 2 3 19. y 21. y u −u u−v −v x x 23. (a) 2 3u 2 3 4, 9 2, 5 8 3, 6 4, 9 5 2, 5 2, 14 18, 7 25. v 3 2 2i j 3i 3, 3 2j 3 2 (b) v (c) 2u u 5v 2 4, 9 y 1 v = 2u x 3 2 3 u −1 −2 −3 3 u 2 27. v 2i 4i j 3j 2i 4, 3 2j 4 y 29. u1 v = u + 2w 4 2 u1 u2 3 3 5 1 u2 v 2w 2 x u −2 4 6 Q...
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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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