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מדריכי לימוד > Precalculus II

Solutions for Vectors

Solutions to Try Its

1. A vector from the origin to (3,5) - a line with an arrow at the (3,5) endpoint. 2. 3u=⟨15,12⟩3u=\langle 15,12\rangle 3. u=8i−11ju=8i - 11j 4. v=34cos⁡(59∘)i+34sin⁡(59∘)jv=\sqrt{34}\cos \left(59^\circ \right)i+\sqrt{34}\sin \left(59^\circ \right)j Magnitude = 34\sqrt{34} θ=tan⁡−1(53)=59.04∘\theta ={\tan }^{-1}\left(\frac{5}{3}\right)=59.04^\circ

Solutions to Odd-Numbered Exercises

1. lowercase, bold letter, usually u, v, w 3. They are unit vectors. They are used to represent the horizontal and vertical components of a vector. They each have a magnitude of 1. 5. The first number always represents the coefficient of the i, and the second represents the j. 7. ⟨7,−5⟩\langle 7,−5\rangle 9. not equal 11. equal 13. equal 15. 7i−3j7i−3j 17. −6i−2j−6i−2j 19. u+v=⟨−5,5⟩,u−v=⟨−1,3⟩,2u−3v=⟨0,5⟩u+v=\langle−5,5\rangle,u−v=\langle−1,3\rangle,2u−3v=\langle 0,5\rangle 21. −10i–4j−10i–4j 23. −22929i+52929j−\frac{2\sqrt{29}}{29}i+\frac{5\sqrt{29}}{29}j 25. –2229229i+15229229j–\frac{2\sqrt{229}}{229}i+\frac{15\sqrt{229}}{229}j 27. –72i+210j–\frac{7\sqrt{2}}i+\frac{\sqrt{2}}{10}j 29. ∣v∣=7.810,θ=39.806∘|v|=7.810,\theta=39.806^{\circ} 31. ∣v∣=7.211,θ=236.310∘|v|=7.211,\theta=236.310^{\circ} 33. −6 35. −12 37. 39. Plot of u+v, u-v, and 2u based on the above vectors. In relation to the same origin point, u+v goes to (0,3), u-v goes to (2,-1), and 2u goes to (2,2). 41. Plot of vectors u+v, u-v, and 2u based on the above vectors.Given that u's start point was the origin, u+v starts at the origin and goes to (2,-3); u-v starts at the origin and goes to (4,-1); 2u goes from the origin to (6,-4). 43. Plot of a single vector. Taking the start point of the vector as (0,0) from the above set up, the vector goes from the origin to (-1,-6). 45. Vector extending from the origin to (7,5), taking the base as the origin. 47. ⟨4,1⟩\langle 4,1\rangle 49. v=−7i+3jv=−7i+3j Vector going from (4,-1) to (-3,2). 51. 32i+32j3\sqrt{2}i+3\sqrt{2}j 53. i−3ji−\sqrt{3}j 55. a. 58.7; b. 12.5 57. x=7.13x=7.13 pounds, y=3.63y=3.63 pounds 59. x=2.87x=2.87 pounds, y=4.10y=4.10 pounds 61. 4.635 miles, 17.764∘17.764^{\circ} N of E 63. 17 miles. 10.318 miles 65. Distance: 2.868. Direction: 86.474∘86.474^{\circ} North of West, or 3.526∘3.526^{\circ} West of North 67. 4.924∘4.924^{\circ}. 659 km/hr 69. 4.424∘4.424^{\circ} 71. (0.081, 8.602) 73. 21.801∘21.801^{\circ}, relative to the car’s forward direction 75. parallel: 16.28, perpendicular: 47.28 pounds 77. 19.35 pounds, 231.54∘231.54^{\circ} from the horizontal 79. 5.1583 pounds, 75.8∘75.8^{\circ} from the horizontal

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