Math · Drill 48

Math practice 48

105 questions ~15 min recommended

⏱ 00:00

Score

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1. Which vector represents $4\mathbf{b}$ if $\mathbf{b} = \langle 0, 7 \rangle$?

A. $$\langle 4, 28 \rangle$

B. $$\langle 4, 7 \rangle$

C. $$\langle 0, 28 \rangle$

D. $$\langle 0, 7 \rangle$

2. What is the magnitude of vector $\mathbf{v}$ if $\mathbf{v} = \langle 5, 12 \rangle$?

A. 13

B. 17

C. 18

D. 25

3. What is the magnitude of the vector $\langle 3, 4\rangle$?

A. $$7$

B. $$\sqrt{7}$

C. $$5$

D. $$25$

4. What is $\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle -2, 5\rangle$ and $\mathbf{w}=\langle 6, -1\rangle$?

A. $$\langle 4, -6\rangle$

B. $$\langle -8, 6\rangle$

C. $$\langle 8, -6\rangle$

D. $$\langle 4, 4\rangle$

5. If $\mathbf{v} = \langle 7, 1 \rangle$ and $\mathbf{w} = \langle 1, 7 \rangle$, what is $\mathbf{v} - \mathbf{w}$?

A. \langle 8, 8 \rangle

B. \langle 6, 6 \rangle

C. \langle -6, 6 \rangle

D. \langle 6, -6 \rangle

6. What is $\mathbf{v} + \mathbf{w}$ if $\mathbf{v} = \langle 1, 2 \rangle$ and $\mathbf{w} = \langle 3, 4 \rangle$?

A. $$\langle 4, 6 \rangle$

B. $$\langle 2, 6 \rangle$

C. $$\langle 3, 6 \rangle$

D. $$\langle 1, 4 \rangle$

7. What is the magnitude of $\mathbf{c} = \langle 8, 15 \rangle$?

A. 17

B. 23

C. 64

D. 225

8. What is the magnitude of the vector $\langle 8, 6\rangle$?

A. $$\sqrt{14}$

B. $$10$

C. $$14$

D. $$100$

9. What is $-3\mathbf{v}$ if $\mathbf{v}=\langle 2, -4\rangle$?

A. $$\langle -6, -12\rangle$

B. $$\langle 6, 12\rangle$

C. $$\langle 2, 12\rangle$

D. $$\langle -6, 12\rangle$

10. What is $4\mathbf{v}$ if $\mathbf{v} = \langle 0, 5 \rangle$?

A. \langle 0, 20 \rangle

B. \langle 0, 5 \rangle

C. \langle 0, 25 \rangle

D. \langle 4, 20 \rangle

11. What is $\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle -3, -7\rangle$ and $\mathbf{w}=\langle 5, 2\rangle$?

A. $$\langle -8, -9\rangle$

B. $$\langle 2, -5\rangle$

C. $$\langle 8, 9\rangle$

D. $$\langle 2, 9\rangle$

12. What is $\mathbf{v}-\mathbf{w}$ if $\mathbf{v}=\langle 7, -3\rangle$ and $\mathbf{w}=\langle -1, 4\rangle$?

A. $$\langle 8, 1\rangle$

B. $$\langle -8, 7\rangle$

C. $$\langle 6, 1\rangle$

D. $$\langle 8, -7\rangle$

13. Which vector represents moving 4 units left and 2 units up?

A. $$\langle -4, -2\rangle$

B. $$\langle -4, 2\rangle$

C. $$\langle 2, -4\rangle$

D. $$\langle 4, 2\rangle$

14. What is $\tfrac{1}{2}\mathbf{v}$ if $\mathbf{v}=\langle 10, -8\rangle$?

A. $$\langle 5, -4\rangle$

B. $$\langle 5, 4\rangle$

C. $$\langle 20, -16\rangle$

D. $$\langle 10, -4\rangle$

15. What is $3\mathbf{v}$ if $\mathbf{v}=\langle -3, -6\rangle$?

A. $$\langle -9, -6\rangle$

B. $$\langle -9, -18\rangle$

C. $$\langle 9, 18\rangle$

D. $$\langle -6, -12\rangle$

16. What is the magnitude of $\mathbf{v} = \langle 12, 5 \rangle$?

A. 13

B. 17

C. 17

D. 144

17. A force vector is $\mathbf{v}=\langle 4, -9\rangle$. What is $3\mathbf{v}$?

A. $$\langle 12, -27\rangle$

B. $$\langle 7, -27\rangle$

C. $$\langle -12, 27\rangle$

D. $$\langle 12, -9\rangle$

18. A robot moves first by $\langle -4, 7\rangle$ and then by $\langle 6, -3\rangle$. Which vector represents the robot’s net movement?

A. $$\langle -10, 10\rangle$

B. $$\langle 10, -10\rangle$

C. $$\langle 2, -10\rangle$

D. $$\langle 2, 4\rangle$

19. A boat’s velocity is $v=\langle -2,1\rangle$ (in m/s). Which vector represents the opposite direction with the same speed?

A. $$\langle 2,-1\rangle$

B. $$\langle -1,2\rangle$

C. $$\langle -2,-1\rangle$

D. $$\langle 2,1\rangle$

20. In the standard $(x, y)$ coordinate plane, $\vec{u} = \langle 2, -5 \rangle$ and $\vec{v} = \langle -3, 1 \rangle$. What is the magnitude of the vector $\vec{u} + \vec{v}$?

A. $$\sqrt{41}$

B. $$5$

C. $$\sqrt{17}$

D. $$\sqrt{37}$

21. Which vector represents the direction of $\mathbf{u} = \langle 4, 3 \rangle$ as a unit vector?

A. $$\langle \frac{4}{5}, \frac{3}{5} \rangle$

B. $$\langle 4, 3 \rangle$

C. $$\langle \frac{3}{5}, \frac{4}{5} \rangle$

D. $$\langle \frac{3}{4}, \frac{4}{3} \rangle$

22. Which vector represents $\mathbf{x} + \mathbf{y}$ if $\mathbf{x} = \langle 2, 3 \rangle$ and $\mathbf{y} = \langle 4, -1 \rangle$?

A. $$\langle 6, 2 \rangle$

B. $$\langle 2, -2 \rangle$

C. $$\langle 2, 4 \rangle$

D. $$\langle 6, 4 \rangle$

23. What is $2\mathbf{u} + 3\mathbf{v}$ if $\mathbf{u} = \langle 1, 1 \rangle$ and $\mathbf{v} = \langle 2, 3 \rangle$?

A. $$\langle 6, 9 \rangle$

B. $$\langle 5, 8 \rangle$

C. $$\langle 8, 11 \rangle$

D. $$\langle 7, 11 \rangle$

24. What is $\mathbf{v} + \mathbf{w}$ if $\mathbf{v} = \langle -2, 5 \rangle$ and $\mathbf{w} = \langle 3, 7 \rangle$?

A. $$\langle 0, 12 \rangle$

B. $$\langle 1, 12 \rangle$

C. $$\langle 1, 2 \rangle$

D. $$\langle 5, 12 \rangle$

25. Which vector represents the direction of $\mathbf{w} = \langle 6, 8 \rangle$ as a unit vector?

A. $$\langle 3, 4 \rangle$

B. $$\langle \frac{3}{5}, \frac{4}{5} \rangle$

C. $$\langle \frac{4}{5}, \frac{3}{5} \rangle$

D. $$\langle 6, 8 \rangle$

26. What is $\mathbf{u} + 2\mathbf{v}$ if $\mathbf{u} = \langle 3, -1 \rangle$ and $\mathbf{v} = \langle 1, 4 \rangle$?

A. $$\langle 5, 7 \rangle$

B. $$\langle 5, 8 \rangle$

C. $$\langle 4, 7 \rangle$

D. $$\langle 3, 7 \rangle$

27. What is $-2\mathbf{w}$ if $\mathbf{w} = \langle -3, 5 \rangle$?

A. $$\langle 6, -10 \rangle$

B. $$\langle 6, 10 \rangle$

C. $$\langle -6, -10 \rangle$

D. $$\langle -6, 10 \rangle$

28. What is $3\mathbf{v}$ if $\mathbf{v} = \langle 2, -1 \rangle$?

A. $$\langle 6, -3 \rangle$

B. $$\langle 2, -3 \rangle$

C. $$\langle 2, 3 \rangle$

D. $$\langle 6, 3 \rangle$

29. What is the magnitude of $\mathbf{x} = \langle 9, 12 \rangle$?

A. 15

B. 21

C. 81

D. 144

30. What is $0.5\mathbf{a}$ if $\mathbf{a} = \langle 10, 6 \rangle$?

A. $$\langle 10, 3 \rangle$

B. $$\langle 0, 0 \rangle$

C. $$\langle 5, 3 \rangle$

D. $$\langle 5, 6 \rangle$

31. What is the magnitude of $\mathbf{y} = \langle 7, 24 \rangle$?

A. 25

B. 31

C. 49

D. 576

32. What is $\mathbf{v} - \mathbf{w}$ if $\mathbf{v} = \langle 6, -4 \rangle$ and $\mathbf{w} = \langle -2, 5 \rangle$?

A. $$\langle 8, -9 \rangle$

B. $$\langle 4, -9 \rangle$

C. $$\langle 8, 9 \rangle$

D. $$\langle -8, -9 \rangle$

33. What is $\mathbf{u} \cdot \mathbf{v}$ if $\mathbf{u} = \langle 3, -2 \rangle$ and $\mathbf{v} = \langle 4, 5 \rangle$?

A. 2

B. 7

C. 22

D. 23

34. What is the magnitude of vector $\mathbf{v} = \langle 3, 4 \rangle$?

A. 5

B. 6

C. 7

D. 25

35. What is $\mathbf{v} - \mathbf{u}$ if $\mathbf{v} = \langle 7, 2 \rangle$ and $\mathbf{u} = \langle 4, 5 \rangle$?

A. $$\langle -3, -7 \rangle$

B. $$\langle 11, -3 \rangle$

C. $$\langle 3, 7 \rangle$

D. $$\langle 3, -3 \rangle$

36. Which vector represents the addition of $\mathbf{a} = \langle 5, -3 \rangle$ and $\mathbf{b} = \langle -2, 4 \rangle$?

A. $$\langle -7, 1 \rangle$

B. $$\langle 3, 1 \rangle$

C. $$\langle 7, 1 \rangle$

D. $$\langle 3, 7 \rangle$

37. What is the magnitude of $\mathbf{a} = \langle -5, 0 \rangle$?

A. 0

B. 5

C. 10

D. 25

38. What is $\mathbf{v} \cdot \mathbf{w}$ if $\mathbf{v} = \langle 0, 9 \rangle$ and $\mathbf{w} = \langle 4, -3 \rangle$?

A. -27

B. 0

C. 12

D. 36

39. What is the magnitude of $\mathbf{b} = \langle 0, -13 \rangle$?

A. 0

B. 13

C. 26

D. 169

40. If $\mathbf{v} = \langle 9, -3 \rangle$ and $\mathbf{w} = \langle -2, 4 \rangle$, what is $\mathbf{v} + \mathbf{w}$?

A. \langle 7, 7 \rangle

B. \langle 7, 1 \rangle

C. \langle 11, 1 \rangle

D. \langle 7, -7 \rangle

41. Which vector represents a unit vector in the same direction as $\mathbf{v} = \langle 3, 4 \rangle$?

A. \langle 0.6, 0.8 \rangle

B. \langle 6, 8 \rangle

C. \langle 1.5, 2 \rangle

D. \langle 3, 4 \rangle

42. What is the magnitude of $\mathbf{v}$ if $\mathbf{v} = \langle 6, 8 \rangle$?

A. 10

B. 14

C. 48

D. 100

43. What is the magnitude of vector $\mathbf{v}$ if $\mathbf{v} = \langle 8, 15 \rangle$?

A. 17

B. 23

C. 64

D. 225

44. What is $\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle -4, -6\rangle$ and $\mathbf{w}=\langle 9, -1\rangle$?

A. $$\langle 5, 5\rangle$

B. $$\langle 5, -7\rangle$

C. $$\langle -13, -7\rangle$

D. $$\langle -5, -7\rangle$

45. What is $-2\mathbf{v}$ if $\mathbf{v}=\langle 9, -4\rangle$?

A. $$\langle -18, 8\rangle$

B. $$\langle -18, -8\rangle$

C. $$\langle -2, 8\rangle$

D. $$\langle 18, 8\rangle$

46. What is $4\mathbf{v}$ if $\mathbf{v}=\langle 1, -7\rangle$?

A. $$\langle 4, -28\rangle$

B. $$\langle -4, 28\rangle$

C. $$\langle 5, -21\rangle$

D. $$\langle 4, -7\rangle$

47. What is $\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle 2, 9\rangle$ and $\mathbf{w}=\langle 4, -7\rangle$?

A. $$\langle 8, -16\rangle$

B. $$\langle 6, 2\rangle$

C. $$\langle -2, 2\rangle$

D. $$\langle 6, 16\rangle$

48. What is $\frac{1}{2}$ times $v$ if $v=\langle 8,-6\rangle$?

A. $$\langle 16,-12\rangle$

B. $$\langle 4,3\rangle$

C. $$\langle 8,-3\rangle$

D. $$\langle 4,-3\rangle$

49. What is the magnitude of $\mathbf{a} = \langle 9, 12 \rangle$?

A. 15

B. 21

C. 144

D. 225

50. If $\mathbf{v} = \langle 5, 12 \rangle$, what is $-\mathbf{v}$?

A. $$\langle -5, -12 \rangle$

B. $$\langle 5, -12 \rangle$

C. $$\langle 0, 0 \rangle$

D. $$\langle -5, 12 \rangle$

51. What is the magnitude of $\mathbf{u} = \langle -6, 8 \rangle$?

A. 10

B. 14

C. 28

D. 100

52. What is $\mathbf{u} \cdot \mathbf{v}$ if $\mathbf{u} = \langle 5, 6 \rangle$ and $\mathbf{v} = \langle 3, 4 \rangle$?

A. 38

B. 39

C. 42

D. 50

53. What is $2\mathbf{v}$ if $\mathbf{v} = \langle 3, 5 \rangle$?

A. \langle 6, 5 \rangle

B. \langle 9, 15 \rangle

C. \langle 3, 10 \rangle

D. \langle 6, 10 \rangle

54. What is $\mathbf{x} - \mathbf{y}$ if $\mathbf{x} = \langle -8, 3 \rangle$ and $\mathbf{y} = \langle -5, -7 \rangle$?

A. $$\langle -13, 10 \rangle$

B. $$\langle -13, -10 \rangle$

C. $$\langle -3, -4 \rangle$

D. $$\langle -3, 10 \rangle$

55. What is $\mathbf{u} + \mathbf{v}$ if $\mathbf{u} = \langle 1, 2 \rangle$ and $\mathbf{v} = \langle 3, -2 \rangle$?

A. $$\langle 4, 4 \rangle$

B. $$\langle 4, 0 \rangle$

C. $$\langle 2, 0 \rangle$

D. $$\langle 2, 4 \rangle$

56. What is the magnitude of vector $\mathbf{v}$ if $\mathbf{v} = \langle 1, \sqrt{3} \rangle$?

A. 1

B. 2

C. 3

D. 4

57. If $\mathbf{v} = \langle 10, -5 \rangle$ and $\mathbf{w} = \langle -3, 2 \rangle$, what is $\mathbf{v} + \mathbf{w}$?

A. \langle 13, -3 \rangle

B. \langle 7, -7 \rangle

C. \langle 13, -7 \rangle

D. \langle 7, -3 \rangle

58. What is $-3\mathbf{v}$ if $\mathbf{v}=\langle -2, 5\rangle$?

A. $$\langle -2, -15\rangle$

B. $$\langle -6, -15\rangle$

C. $$\langle 6, 15\rangle$

D. $$\langle 6, -15\rangle$

59. What is $\mathbf{v}-\mathbf{w}$ if $\mathbf{v}=\langle 7, 1\rangle$ and $\mathbf{w}=\langle 2, -3\rangle$?

A. $$\langle -5, 4\rangle$

B. $$\langle 5, 4\rangle$

C. $$\langle 5, -2\rangle$

D. $$\langle 9, -2\rangle$

60. What is $\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle 3, -2\rangle$ and $\mathbf{w}=\langle -5, 4\rangle$?

A. $$\langle -8, 2\rangle$

B. $$\langle -2, -2\rangle$

C. $$\langle 8, -6\rangle$

D. $$\langle -2, 2\rangle$

61. What is $\tfrac{1}{2}\mathbf{v}$ if $\mathbf{v}=\langle -8, 10\rangle$?

A. $$\langle -4, 5\rangle$

B. $$\langle -16, 20\rangle$

C. $$\langle -4, 10\rangle$

D. $$\langle 4, -5\rangle$

62. What is $\mathbf{v}-\mathbf{w}$ if $\mathbf{v}=\langle -1, 8\rangle$ and $\mathbf{w}=\langle 6, 3\rangle$?

A. $$\langle -7, 5\rangle$

B. $$\langle -7, 11\rangle$

C. $$\langle 7, 5\rangle$

D. $$\langle 5, 11\rangle$

63. Which vector represents moving 3 units left and 5 units up on a coordinate plane?

A. $$\langle -3, -5\rangle$

B. $$\langle 3, 5\rangle$

C. $$\langle -3, 5\rangle$

D. $$\langle 5, -3\rangle$

64. What is the magnitude of $\mathbf{v}$ if $\mathbf{v}=\langle 8, -15\rangle$?

A. $$23$

B. $$17$

C. $$\sqrt{289}$

D. $$\sqrt{8+15}$

65. What is $\mathbf{v}-\mathbf{w}$ if $\mathbf{v}=\langle 10, -2\rangle$ and $\mathbf{w}=\langle -3, 5\rangle$?

A. $$\langle 7, 3\rangle$

B. $$\langle -13, 7\rangle$

C. $$\langle 13, -7\rangle$

D. $$\langle 13, 7\rangle$

66. What is the magnitude of $\mathbf{v}$ if $\mathbf{v}=\langle 5, 12\rangle$?

A. $$\sqrt{169}$

B. $$\sqrt{17}$

C. $$13$

D. $$17$

67. Which vector represents moving 4 units right and 2 units down on a coordinate plane?

A. $$\langle 4, -2\rangle$

B. $$\langle -4, 2\rangle$

C. $$\langle 4, 2\rangle$

D. $$\langle 2, -4\rangle$

68. If $\mathbf{v} = \langle -6, 2 \rangle$ and $\mathbf{w} = \langle 3, 4 \rangle$, what is $\mathbf{v} - \mathbf{w}$?

A. \langle -9, -2 \rangle

B. \langle 3, -2 \rangle

C. \langle -3, -2 \rangle

D. \langle -9, 2 \rangle

69. What is the magnitude of vector $\mathbf{v}$ if $\mathbf{v} = \langle 3, 4 \rangle$?

A. 5

B. 7

C. 7.07

D. 25

70. What is $5\mathbf{v}$ if $\mathbf{v} = \langle -1, 6 \rangle$?

A. $$\langle 5, 30 \rangle$

B. $$\langle -5, 6 \rangle$

C. $$\langle -1, 30 \rangle$

D. $$\langle -5, 30 \rangle$

71. If $\mathbf{v} = \langle 1, 4 \rangle$ and $\mathbf{w} = \langle 5, -2 \rangle$, what is $\mathbf{v} - \mathbf{w}$?

A. \langle -4, 6 \rangle

B. \langle -4, 2 \rangle

C. \langle 4, 6 \rangle

D. \langle 6, 2 \rangle

72. A hiker walks $\langle 5, -1\rangle$ miles one day and then $\langle -2, 4\rangle$ miles the next day. What is the total displacement vector for the two days?

A. $$\langle 3, 3\rangle$

B. $$\langle 7, -5\rangle$

C. $$\langle -7, 5\rangle$

D. $$\langle 3, -5\rangle$

73. A force is modeled by the vector $\langle -8, 6\rangle$. What is the magnitude of the vector $\langle -8, 6\rangle$?

A. $$\sqrt{10}$

B. $$\sqrt{28}$

C. $$100$

D. $$10$

74. What is the magnitude of $\mathbf{v}$ if $\mathbf{v}=\langle 9, 12\rangle$?

A. $$15$

B. $$\sqrt{21}$

C. $$\sqrt{225}$

D. $$225$

75. A drone’s horizontal displacement is represented by the vector $\langle 6, 8\rangle$. What is the magnitude of the vector $\langle 6, 8\rangle$?

A. $$\sqrt{28}$

B. $$\sqrt{100}$

C. $$10$

D. $$14$

76. What is $k\mathbf{v}$ if $\mathbf{v}=\langle -5, -4\rangle$ and $k=2$?

A. $$\langle -5, -8\rangle$

B. $$\langle 10, 8\rangle$

C. $$\langle -10, -2\rangle$

D. $$\langle -10, -8\rangle$

77. A force is represented by the vector $\mathbf{v}=\langle 7,\,-4\rangle$. What is $3\mathbf{v}$?

A. $$\langle 21,\,-4\rangle$

B. $$\langle -21,\,12\rangle$

C. $$\langle 21,\,-12\rangle$

D. $$\langle 10,\,-1\rangle$

78. Two vectors are $\mathbf{v}=\langle -8,\,3\rangle$ and $\mathbf{w}=\langle 1,\,6\rangle$. What is $\mathbf{v}-\mathbf{w}$?

A. $$\langle -7,\,9\rangle$

B. $$\langle -9,\,3\rangle$

C. $$\langle 9,\,3\rangle$

D. $$\langle -9,\,-3\rangle$

79. A hiker walks with displacement vector $\mathbf{v}=\langle -3,\,5\rangle$ and then $\mathbf{w}=\langle 4,\,-2\rangle$. What is $\mathbf{v}+\mathbf{w}$?

A. $$\langle -7,\,7\rangle$

B. $$\langle 1,\,-7\rangle$

C. $$\langle -1,\,3\rangle$

D. $$\langle 1,\,3\rangle$

80. A drone’s horizontal movement is represented by the vector $\langle 6,\,8\rangle$. What is the magnitude of the vector $\langle 6,\,8\rangle$?

A. $$10$

B. $$14$

C. $$\sqrt{28}$

D. $$\sqrt{100}$

81. A robot’s movement vector is $\mathbf{v}=\langle 9,\,12\rangle$. What is the magnitude of $\mathbf{v}$?

A. $$\sqrt{33}$

B. $$\sqrt{225}$

C. $$15$

D. $$21$

82. A boat’s velocity relative to the water is $\mathbf{v}=\langle 5,\,1\rangle$, and the current is $\mathbf{w}=\langle -2,\,3\rangle$. What is the resulting velocity $\mathbf{v}+\mathbf{w}$?

A. $$\langle -3,\,4\rangle$

B. $$\langle 7,\,-2\rangle$

C. $$\langle 3,\,-2\rangle$

D. $$\langle 3,\,4\rangle$

83. A wind vector is $\mathbf{v}=\langle 3,\,-4\rangle$. Which vector represents the same direction but with twice the magnitude?

A. $$\langle -6,\,8\rangle$

B. $$\langle 6,\,-8\rangle$

C. $$\langle 1.5,\,-2\rangle$

D. $$\langle 6,\,8\rangle$

84. A delivery route is modeled by vectors $\mathbf{v}=\langle 4,\,9\rangle$ and $\mathbf{w}=\langle -6,\,2\rangle$. What is $\mathbf{v}+\mathbf{w}$?

A. $$\langle 10,\,7\rangle$

B. $$\langle -2,\,7\rangle$

C. $$\langle -2,\,11\rangle$

D. $$\langle -10,\,11\rangle$

85. A skier’s displacement changes from $\mathbf{v}=\langle 2, -6\rangle$ to $\mathbf{w}=\langle -5, 1\rangle$. What is $\mathbf{v}-\mathbf{w}$?

A. $$\langle 3, 5\rangle$

B. $$\langle -3, -5\rangle$

C. $$\langle -7, 7\rangle$

D. $$\langle 7, -7\rangle$

86. A robot moves by $\mathbf{v}=\langle 9, -4\rangle$ and then by $\mathbf{w}=\langle -3, -7\rangle$. What is $\mathbf{v}+\mathbf{w}$?

A. $$\langle 6, -11\rangle$

B. $$\langle -12, -3\rangle$

C. $$\langle 6, 3\rangle$

D. $$\langle 12, 3\rangle$

87. A displacement is represented by $\mathbf{v}=\langle 2,\,-7\rangle$. What is $-2\mathbf{v}$?

A. $$\langle -4,\,14\rangle$

B. $$\langle -4,\,-14\rangle$

C. $$\langle 4,\,-14\rangle$

D. $$\langle -2,\,7\rangle$

88. A vector is $\langle -5,\,12\rangle$. What is the magnitude of vector $\langle -5,\,12\rangle$?

A. $$13$

B. $$\sqrt{17}$

C. $$17$

D. $$\sqrt{169}$

89. Which vector represents moving 4 units left and 2 units up on a coordinate plane?

A. $$\langle 2, -4\rangle$

B. $$\langle 4, 2\rangle$

C. $$\langle -4, 2\rangle$

D. $$\langle -2, 4\rangle$

90. What is $-2\mathbf{v}$ if $\mathbf{v}=\langle -7, 3\rangle$?

A. $$\langle 14, -6\rangle$

B. $$\langle 14, 6\rangle$

C. $$\langle -9, 1\rangle$

D. $$\langle -14, 6\rangle$

91. What is $v+w$ if $v=\langle 3,-5\rangle$ and $w=\langle -2,7\rangle$?

A. $$\langle 1,2\rangle$

B. $$\langle -1,2\rangle$

C. $$\langle 5,12\rangle$

D. $$\langle 1,-12\rangle$

92. Which vector represents the displacement from point $A(2,-1)$ to point $B(-3,5)$?

A. $$\langle 1,-4\rangle$

B. $$\langle 5,-6\rangle$

C. $$\langle -1,4\rangle$

D. $$\langle -5,6\rangle$

93. What is $-3$ times $v$ if $v=\langle -4,2\rangle$?

A. $$\langle -12,6\rangle$

B. $$\langle 12,2\rangle$

C. $$\langle 12,-6\rangle$

D. $$\langle -7, -1\rangle$

94. What is $v-w$ if $v=\langle -1,4\rangle$ and $w=\langle 6,-3\rangle$?

A. $$\langle -7,7\rangle$

B. $$\langle 5,1\rangle$

C. $$\langle 7,-7\rangle$

D. $$\langle -7,1\rangle$

95. What is the magnitude of vector $\mathbf{v}$ if $\mathbf{v} = \langle 7, 24 \rangle$?

A. 25

B. 31

C. 49

D. 576

96. What is $3\mathbf{u} - \mathbf{v}$ if $\mathbf{u} = \langle 2, 4 \rangle$ and $\mathbf{v} = \langle 1, -1 \rangle$?

A. $$\langle 5, 13 \rangle$

B. $$\langle 6, 13 \rangle$

C. $$\langle 5, 11 \rangle$

D. $$\langle 7, 11 \rangle$

97. What is $-2\mathbf{v}$ if $\mathbf{v} = \langle 5, -1 \rangle$?

A. $$\langle 10, -2 \rangle$

B. $$\langle -10, -1 \rangle$

C. $$\langle -10, 2 \rangle$

D. $$\langle 5, 2 \rangle$

98. What is the magnitude of $\mathbf{v}$ if $\mathbf{v}=\langle 6, 8\rangle$?

A. $$10$

B. $$\sqrt{100}$

C. $$14$

D. $$\sqrt{6^2+8^2}=\sqrt{28}$

99. What is $k\mathbf{v}$ if $\mathbf{v}=\langle 4, -6\rangle$ and $k=-2$?

A. $$\langle 4, 12\rangle$

B. $$\langle 8, -12\rangle$

C. $$\langle -8, 12\rangle$

D. $$\langle -8, -12\rangle$

100. What is $\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle -3, 5\rangle$ and $\mathbf{w}=\langle 7, -2\rangle$?

A. $$\langle 10, -7\rangle$

B. $$\langle 4, -7\rangle$

C. $$\langle 4, 3\rangle$

D. $$\langle -10, 7\rangle$

101. A velocity vector is $\mathbf{v}=\langle -7, 3\rangle$. What is $3\mathbf{v}$?

A. $$\langle 21, -9\rangle$

B. $$\langle -7, 9\rangle$

C. $$\langle -21, 9\rangle$

D. $$\langle -21, 3\rangle$

102. A velocity vector is $\mathbf{v}=\langle -8, 6\rangle$. What is the magnitude of $\mathbf{v}$?

A. $$10$

B. $$\sqrt{28}$

C. $$\sqrt{100}$

D. $$14$

103. What is the magnitude of the vector $\langle 1, -\!\sqrt{3}\rangle$?

A. $$\sqrt{3}$

B. $$\sqrt{2}$

C. $$2$

D. $$4$

104. What is $2\mathbf{v}+\mathbf{w}$ if $\mathbf{v}=\langle 1, -3\rangle$ and $\mathbf{w}=\langle -4, 5\rangle$?

A. $$\langle -2, 11\rangle$

B. $$\langle 6, -11\rangle$

C. $$\langle -2, -1\rangle$

D. $$\langle -6, 11\rangle$

105. In the standard $(x, y)$ coordinate plane, $\vec{u} = \langle 2, -5 \rangle$ and $\vec{v} = \langle -3, 1 \rangle$. What is the magnitude of the vector $\vec{u} + \vec{v}$?

A. $$\sqrt{37}$

B. $$5$

C. $$\sqrt{17}$

D. $$\sqrt{41}$

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