Solutions: 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

3. u=8i11j

4. v=34cos(59)i+34sin(59)j
Magnitude = 34
θ=tan1(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. 7i3j

17. 6i2j

19. u+v=5,5,uv=1,3,2u3v=0,5

21. 10i4j

23. 22929i+52929j

25. 2229229i+15229229j

27. 72i+210j

29. |v|=7.810,θ=39.806

31. |v|=7.211,θ=236.310

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

49. v=7i+3j
Vector going from (4,-1) to (-3,2).

51. 32i+32j

53. i3j

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