R 2 z x 2 y2 81 r 5 83 5 sphere matches graph c z

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Unformatted text preview: the plane z Review Exercises for Chapter 10 1. P (a) u v (b) v (c) 2u v 1, 2 , Q \ 4, 1 , R 3, 4, 2 1 4i 25 3i 5, 4 j, 2j 3. v v cos i v sin j 8 cos 120 i 4i 4 3j 8 sin 120 j PQ \ PR 42 22 6, 2 4, 2 10, 0 10i Review Exercises for Chapter 10 5. 120 cos 100 arccos tan y 5 6 2 tan 2 11 5 5, 4, 0 10 11 3.015 ft y 120 lb 100 lb 2 ft 257 2 ⇒y y θ 2 tan arccos 5 6 4, x 5: 7. z 0, y 9. Looking down from the positive x-axis towards the yz-plane, the point is either in the first quadrant y > 0, z > 0 or in the third quadrant y < 0, z < 0 . The x-coordinate can be any number. 15 2 z2 2 11. x 3 2 y 2 2 z 6 2 13. x2 x 4x 2 2 4 y 3 y2 2 6y z2 9 9 4 4 9 15. v 4 z 2, 4 1, 7 3 2, 5, 10 Center: 2, 3, 0 Radius: 3 z 4 3 2 (2, − 1, 3) 3 2 1 12 3 5 5 x 4 3 −2 y 6 x 5 4 3 45 6 y (4, 4, − 7) 17. v w Since 21. P (a) u v (b) u (c) v 5 1 3, 6 3, 3 4, 9 4, 6 1 1 4, 2, 10 2, 1, 5 19. Unit vector: u u 2, 3, 5 38 2 , 38 3 , 38 5 38 2w v, the points lie in a straight line. 4, 4, 0 , R 1, 4, 0 3, 0, 6 1 9 3 i 4 2 i 3 36 3 45 3 j 4 2 j 3 3 52 2 i 40 i 3i 2, 0, 6 4j, 6k 06 3 23. u 7, 2, 3 , v v 1, 4, 5 5, 0, 0 , Q \ PQ \ Since u 0, the vectors are orthogonal. PR v v 25. u v u u v cos 5 cos 2 cos v 5 2 sin sin i 3j j 27. u 10, 5, 15 , v 2, 1, 3 u 5v ⇒ u is parallel to v and in the opposite direction. 52 1 2 uv uv arccos 2 5 22 1 52 6 4 15 3 2 4 6 258 Chapter 10 Vectors and the Geometry of Space ± 6, 29. There are many correct answers. For example: v 5, 0 . In Exercises 31–39, u 31. u u 33 14 2 14 < 2 3, 2 2, 1 , v 11 u 2 > < 2, 4, 3,w > < 1, 2, 2 . 33. projuw u u w 2 > u 2, 1 5 14 5 14 5 3, 14 15 10 ,, 14 14 15 5 ,, 14 7 i 2 1 j 4 2 k 3 2 35. n n n n v w 5 1 5 2i 2i j 37. V u 3, v w 2, 1, 0 4 4 2, 1 j 39. Area parallelogram u v 102 285 112 8 2 (See Exercises 36, 38) 41. F \ c cos 20 j 2k F \ sin 20 k PQ z PQ \ PQ 200 c F F 43. v j i 0 0 F j k 0 2 c cos 20 c sin 20 2c cos 20 2 ft 70° F 2c cos 20 i y PQ 100 cos 20 x 100 cos 20 j cos 20 100 1 tan2 20 sin 20 k 100 j tan 20 k 100 sec 20 106.4 lb 45. 3x 3y 7z 4,...
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