818 CHAPTER 8 Applications of Trigonometry 24. v 3 1308 x y 0 25. v 5 –358 x y 0 26. v 2 –1408 x y 0 30. –8 4 –8 4 u v x y 31. –8 4 –4 4 u v x y 32. 8 –4 –8 8 u v x y 27. –4 4 –8 4 u v x y 28. 8 –4 4 v u x y 29. –4 4 –8 4 u v x y Use the figure to find each vector: (a) u + v (b) u - v (c) -u. Use vector notation as in Example 4. Given u = 8-2, 59 and v = 84, 39, find each of the following. See Example 4. 33. u - v 34. v - u 35. -4u 36. -5v 37. 3u - 6v 38. -2u + 4v 39. u + v - 3u 40. 2u + v - 6v Given vectors u and v, find: (a) 2u (b) 2u + 3v (c) v - 3u. 41. u = 2i, v = i + j 42. u = -i + 2j, v = i - j 43. u = 8-1, 29, v = 83, 09 44. u = 8-2, -19, v = 8-3, 29 Write each vector in the form ai + bj. 45. 8-5, 89 46. 86, -39 47. 82, 09 48. 80, -49 Find the dot product for each pair of vectors. See Example 5. 49. 86, -19, 82, 59 50. 8-3, 89, 87, -59 51. 85, 29, 8-4, 109 52. 87, -29, 84, 149 53. 4i, 5i - 9j 54. 2i + 4j, -j 58. 84, 09, 82, 29 59. 8-23, 19, 82, -2239 60. 8223, 29, 8-523,59 Find the angle between each pair of vectors. Round to two decimal places as necessary. See Example 6. 55. 82, 19, 8-3, 19 56. 823, 19, 82, 2239 57. 81, 29, 8-6, 39 61. 81, 69, 8-1, 79 62. 81, 79, 81, 19 63. 3i + 4j, j 64. -5i + 12j, 3i + 2j 65. 2i + 2j, -5i - 5j 66. 23i + j, 5j
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