Solutions to Try Its

1.

2. $3u=\langle 15,12\rangle$

3. $u=8i - 11j$

4. $v=\sqrt{34}\cos \left(59^\circ \right)i+\sqrt{34}\sin \left(59^\circ \right)j$
Magnitude = $\sqrt{34}$
$\theta ={\tan }^{-1}\left(\frac{5}{3}\right)=59.04^\circ$

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. $\langle 7,−5\rangle$

9. not equal

11. equal

13. equal

15. $7i−3j$

17. $−6i−2j$

19. $u+v=\langle−5,5\rangle,u−v=\langle−1,3\rangle,2u−3v=\langle 0,5\rangle$

21. $−10i–4j$

23. $−\frac{2\sqrt{29}}{29}i+\frac{5\sqrt{29}}{29}j$

25. $–\frac{2\sqrt{229}}{229}i+\frac{15\sqrt{229}}{229}j$

27. $–\frac{7\sqrt{2}}i+\frac{\sqrt{2}}{10}j$

29. $|v|=7.810,\theta=39.806^{\circ}$

31. $|v|=7.211,\theta=236.310^{\circ}$

33. −6

35. −12

37.

39.

41.

43.

45.

47. $\langle 4,1\rangle$

49. $v=−7i+3j$

51. $3\sqrt{2}i+3\sqrt{2}j$

53. $i−\sqrt{3}j$

55. a. 58.7; b. 12.5

57. $x=7.13$ pounds, $y=3.63$ pounds

59. $x=2.87$ pounds, $y=4.10$ pounds

61. 4.635 miles, $17.764^{\circ}$ N of E

63. 17 miles. 10.318 miles

65. Distance: 2.868. Direction: $86.474^{\circ}$ North of West, or $3.526^{\circ}$ West of North

67. $4.924^{\circ}$. 659 km/hr

69. $4.424^{\circ}$

71. (0.081, 8.602)

73. $21.801^{\circ}$, relative to the car’s forward direction

75. parallel: 16.28, perpendicular: 47.28 pounds

77. 19.35 pounds, $231.54^{\circ}$ from the horizontal

79. 5.1583 pounds, $75.8^{\circ}$ from the horizontal