Then v the vector joining the midpoints is v a 2 b i

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Unformatted text preview: cos v ui u u sin v uj u uv v cos u cos v i sin u sin v j 2 u v cos sin tan w u 2 v cos u 2 v i sin 2 cos 2 j 2 u v cos cos 2 u v tan u v cos Thus, 99. True w u 2 2 v 2 2 and w bisects the angle between u and v. 101. True 103. False ai bj 2a Section 10.2 1. 6 5 4 3 Space Coordinates and Vectors in Space 3. (5, − 2, 2) − 2 3 2 1 1 3 2 −2 −3 12 3 y z z (2, 1, 3) 1 4 x 3 2 (−1, 2, 1) 4 23 4 x y (5, − 2, − 2) Section 10.2 Space Coordinates and Vectors in Space 233 5. A 2, 3, 4 B 1, 2, 2 7. x 3, y 4, z 5: 3, 4, 5 9. y z 0, x 10: 10, 0, 0 11. The z-coordinate is 0. 13. The point is 6 units above the xy-plane. 15. The point is on the plane parallel to the yz-plane that passes through x 4. 17. The point is to the left of the xz-plane. 19. The point is on or between the planes y 3 and y 3. 21. The point x, y, z is 3 units below the xy-plane, and below either quadrant I or III. 23. The point could be above the xy-plane and thus above quadrants II or IV, or below the xy-plane, and thus below quadrants I or III. 25. d 5 25 0 4 2 2 36 0 2 6 0 2 27. d 6 25 1 0 2 2 36 61 2 2 2 4 2 65 29. A 0, 0, 0 , B 2, 2, 1 , C 2, AB AC BC BC 2 4, 4 3 31. A 1, AB 3, 2 , B 5, 16 4 36 4 16 4 1, 2 , C 16 16 0 6 6 2 10 1, 1, 2 4 4 0 AB 2 4 16 36 1 16 9 AC 2 6 35 AC BC Since AB AC , the triangle is isosceles. Right triangle 33. The z-coordinate is changed by 5 units: 0, 0, 5 , 2, 2, 6 , 2, 4, 9 35. 5 2 2 , 9 2 37 , 3 2 3 , 2 3, 5 37. Center: 0, 2, 5 Radius: 2 x x 2 2 2 2 39. Center: Radius: 2, 0, 0 2 10 y 2 2 2 0, 6, 0 1, 3, 0 0 y z2 2 4y z 10z 5 4 0 x 1 3 z 2x 0 2 10 0 y2 25 x y2 z2 6y 41. x2 2x 1 x2 y2 x Center: 1, Radius: 5 3, 4 y2 6y 1 z2 9 2x 6y z2 8z 8z z 1 16 4 2 0 1 25 1 9 16 2 y 3 2 234 43. Chapter 10 9x2 x2 x2 2 x 3 x Center: 1 , 3 1 3 1 9 2 Vectors and the Geometry of Space 9z2 6x 2 x 3 2y 1 2 9y2 y2 18y 2y 1 z 1 1 9 z2 0 2 0 0 1 9 1 1 9 1 45. x2 y2 z2 ≤ 36 z2 y2 y Solid ball of radius 6 centered at origin. 1, 0 Radius: 1 47. (a) v 2 2i (b) 5 4 3 2 −2 1 2 3 x 1 1 2 −3 −2 1 2 3 4 y x 3 z 4i 2j 4 2k 2j 3 2,...
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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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