Solutions to Try Its
1.
2. [latex]3u=\langle 15,12\rangle [/latex]
3. [latex]u=8i - 11j[/latex]
4. [latex]v=\sqrt{34}\cos \left(59^\circ \right)i+\sqrt{34}\sin \left(59^\circ \right)j[/latex]
Magnitude = [latex]\sqrt{34}[/latex]
[latex]\theta ={\tan }^{-1}\left(\frac{5}{3}\right)=59.04^\circ [/latex]
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. [latex]\langle 7,−5\rangle[/latex]
9. not equal
11. equal
13. equal
15. [latex]7i−3j[/latex]
17. [latex]−6i−2j[/latex]
19. [latex]u+v=\langle−5,5\rangle,u−v=\langle−1,3\rangle,2u−3v=\langle 0,5\rangle[/latex]
21. [latex]−10i–4j[/latex]
23. [latex]−\frac{2\sqrt{29}}{29}i+\frac{5\sqrt{29}}{29}j[/latex]
25. [latex]–\frac{2\sqrt{229}}{229}i+\frac{15\sqrt{229}}{229}j[/latex]
27. [latex]–\frac{7\sqrt{2}}i+\frac{\sqrt{2}}{10}j[/latex]
29. [latex]|v|=7.810,\theta=39.806^{\circ}[/latex]
31. [latex]|v|=7.211,\theta=236.310^{\circ}[/latex]
33. −6
35. −12
37.
39.
41.
43.
45.
47. [latex]\langle 4,1\rangle[/latex]
49. [latex]v=−7i+3j[/latex]
51. [latex]3\sqrt{2}i+3\sqrt{2}j[/latex]
53. [latex]i−\sqrt{3}j[/latex]
55. a. 58.7; b. 12.5
57. [latex]x=7.13[/latex] pounds, [latex]y=3.63[/latex] pounds
59. [latex]x=2.87[/latex] pounds, [latex]y=4.10[/latex] pounds
61. 4.635 miles, [latex]17.764^{\circ}[/latex] N of E
63. 17 miles. 10.318 miles
65. Distance: 2.868. Direction: [latex]86.474^{\circ}[/latex] North of West, or [latex]3.526^{\circ}[/latex] West of North
67. [latex]4.924^{\circ}[/latex]. 659 km/hr
69. [latex]4.424^{\circ}[/latex]
71. (0.081, 8.602)
73. [latex]21.801^{\circ}[/latex], relative to the car’s forward direction
75. parallel: 16.28, perpendicular: 47.28 pounds
77. 19.35 pounds, [latex]231.54^{\circ}[/latex] from the horizontal
79. 5.1583 pounds, [latex]75.8^{\circ}[/latex] from the horizontal