Solutions to Try Its
1.
2. 3u=⟨15,12⟩
3. u=8i−11j
4. v=√34cos(59∘)i+√34sin(59∘)j
Magnitude = √34
θ=tan−1(53)=59.04∘
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⟩
9. not equal
11. equal
13. equal
15. 7i−3j
17. −6i−2j
19. u+v=⟨−5,5⟩,u−v=⟨−1,3⟩,2u−3v=⟨0,5⟩
21. −10i–4j
23. −2√2929i+5√2929j
25. –2√229229i+15√229229j
27. –7√2i+√210j
29. |v|=7.810,θ=39.806∘
31. |v|=7.211,θ=236.310∘
33. −6
35. −12
37.
39.
41.
43.
45.
47. ⟨4,1⟩
49. v=−7i+3j
51. 3√2i+3√2j
53. i−√3j
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∘ N of E
63. 17 miles. 10.318 miles
65. Distance: 2.868. Direction: 86.474∘ North of West, or 3.526∘ West of North
67. 4.924∘. 659 km/hr
69. 4.424∘
71. (0.081, 8.602)
73. 21.801∘, relative to the car’s forward direction
75. parallel: 16.28, perpendicular: 47.28 pounds
77. 19.35 pounds, 231.54∘ from the horizontal
79. 5.1583 pounds, 75.8∘ from the horizontal
Candela Citations
- Precalculus. Authored by: OpenStax College. Provided by: OpenStax. Located at: http://cnx.org/contents/fd53eae1-fa23-47c7-bb1b-972349835c3c@5.175:1/Preface. License: CC BY: Attribution