3 1 u a u b u c u d u e u 5 u 2i v u 2 2 the dot

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Unformatted text preview: l amount that the person earned on his products. 9. cos 8 5 cos 20 11. u cos 1, 1 , v uv uv 2 2, 2 0 28 0 3 13. u cos 3i j, v uv uv arccos 2i 4j 1 52 15. u cos 1, 1, 1 , v uv uv arcos 2 3 2, 1, 2 36 61.9 1 2 3 2 10 20 1 52 2j 8 5 13 8 13 65 1 , 2 2 3 98.1 17. u cos 3i 4j, v uv uv arccos 3k 8 13 65 116.3 19. u u u v 4, 0 , v 4 1, 1 0 ⇒ not orthogonal c v ⇒ not parallel Neither 21. u u u 4, 3 , v 23. u u uv j 6k, v 8 i 2j k c v ⇒ not parallel v 0 ⇒ orthogonal c v ⇒ not parallel 0 ⇒ not orthogonal Neither 1, 1 25. u u u v 2, 3, 1 , v 1, c v ⇒ not parallel 0 ⇒ orthogonal S ection 10.3 27. u cos cos cos cos2 i 2j 1 3 2 3 2 3 cos2 cos2 1 9 17 0.7560 or 43.3 1.0644 or 61.0 2.0772 or 119.0 4 9 4 9 1 2k, u 3 29. u cos cos cos cos2 0, 6, 0 3 13 The Dot Product of Two Vectors 4, u 52 2 13 239 2 13 cos2 cos2 0 9 13 4 13 1 31. u cos cos cos 3, 2, 2 3 ⇒ 17 2 ⇒ 17 2 ⇒ 17 50 F1 80 F2 F2 u 33. u cos cos cos 1, 5, 2 u 30 1.7544 or 100.5 0.4205 or 24.1 1.1970 or 68.6 1 ⇒ 30 5 ⇒ 30 2 ⇒ 30 35. F1: C1 F2: C2 F F1 4.3193 5.4183 37. Let s v v cos 5.4183 12, 7, 14.1336 5 length of a side. s, s, s s3 cos cos arccos z 4.3193 10, 5, 3 s s3 1 3 1 3 54.7 108.2126, 59.5246, F cos cos cos 124.310 lb 108.2126 ⇒ F 59.5246 ⇒ F 14.1336 ⇒ F 0, 10, 10 02 cos 1 ⇒ 2 43. w2 u w1 0, 3, 3 0 102 02 102 10 102 29.48 s 61.39 96.53 s x v s y \ 39. OA cos cos 41. w2 0⇒ 90 u w1 6, 7 2, 8 4, 1 102 45 2, 2, 2 2, 1, 1 45. u 2, 3 , v u v u v 2 5, 1 v 13 5, 1 26 15 , 22 51 , 22 (a) w1 (b) w2 w1 240 47. u Chapter 10 2, 1, 2 , v u v v 2 Vectors and the Geometry of Space 0, 3, 4 v 0, 2, 33 44 , 25 25 86 , 25 25 49. u v u1, u2, u3 v1, v2, v3 u1v1 u2v2 u3v3 (a) w1 11 0, 3, 4 25 (b) w2 u w1 51. (a) Orthogonal, 2 (b) Acute, 0 < < 2 u v u v 2 (c) Obtuse, 2 < < 53. See page 738. Direction cosines of v cos , , and v1 , cos v v2 , cos v v1, v2, v3 are v3 . v 55. (a) (b) v u⇒u c v ⇒ u and v are parallel. v 0 ⇒ u and v are the direction angles. See Figure 10.26. v v 0⇒u v2 are ort...
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