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Vectors MCQs — Physics (page 2)

42 multiple-choice questions on Vectors from Physics, each with the correct answer and, where available, a teacher's explanation. Read through them to revise the chapter, then practise the same questions one by one to test yourself.

26. Find vecA vecB for vecA = 5hati + 2hatk and vecB = hati + 3hatj - 2hatk.

  1. 9
  2. -1
  3. 1
  4. 3

Answer: C) 1

Explanation: vecA vecB = AxBx + AyBy + AzBz = (5)(1) + (0)(3) + (2)(-2) = 1. SLO P-11-B-02 · Understanding

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27. A vector has components Ax = 8 and Ay = 6. Its magnitude is:

  1. 100
  2. 2
  3. 10
  4. 14

Answer: C) 10

Explanation: vecA = Ax^2 + Ay^2 = 64 + 36 = 10. SLO P-11-B-01 · Understanding

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28. A vector has components Ax = -5, Ay = 5. The angle it makes with the positive x-axis is:

  1. 142^circ
  2. 135^circ
  3. 225^circ
  4. 315^circ

Answer: B) 135^circ

Explanation: tantheta = AyAx; with the signs of the components the vector is in the correct quadrant, so theta = 135^circ. SLO P-11-B-01 · Understanding

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29. A force of 12 N acts at 60^circ to the x-axis. Its x- and y-components are:

  1. Fx = 3 N, Fy = 5.2 N
  2. Fx = 6 N, Fy = 10.4 N
  3. Fx = 12 N, Fy = 12 N
  4. Fx = 10.4 N, Fy = 6 N

Answer: B) Fx = 6 N, Fy = 10.4 N

Explanation: Fx = Fcostheta, Fy = Fsintheta: Fx = 6 N, Fy = 10.4 N. SLO P-11-B-01 · Understanding

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30. A vector has components Ax = -6 and Ay = 8. Its magnitude is:

  1. 100
  2. 10
  3. 14
  4. 11

Answer: B) 10

Explanation: vecA = Ax^2 + Ay^2 = 36 + 64 = 10. SLO P-11-B-01 · Understanding

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31. hatj hati =

  1. -hatk
  2. 0
  3. hatk
  4. 1

Answer: A) -hatk

Explanation: Using the cyclic order hati to hatj to hatk: hatj hati = -hatk. SLO P-11-B-02 · Understanding

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32. A vector has components Ax = 4, Ay = -4. The angle it makes with the positive x-axis is:

  1. 45^circ
  2. 315^circ
  3. 331^circ
  4. 135^circ

Answer: B) 315^circ

Explanation: tantheta = AyAx; with the signs of the components the vector is in the correct quadrant, so theta = 315^circ. SLO P-11-B-01 · Understanding

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33. A force of 20 N acts at 30^circ to the x-axis. Its x- and y-components are:

  1. Fx = 17.3 N, Fy = 10 N
  2. Fx = 8.66 N, Fy = 5 N
  3. Fx = 20 N, Fy = 20 N
  4. Fx = 10 N, Fy = 17.3 N

Answer: A) Fx = 17.3 N, Fy = 10 N

Explanation: Fx = Fcostheta, Fy = Fsintheta: Fx = 17.3 N, Fy = 10 N. SLO P-11-B-01 · Understanding

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34. Find vecA vecB for vecA = 2hati + 3hatj and vecB = 4hati - hatj.

  1. 8
  2. 5
  3. -5
  4. 7

Answer: B) 5

Explanation: vecA vecB = AxBx + AyBy + AzBz = (2)(4) + (3)(-1) + (0)(0) = 5. SLO P-11-B-02 · Understanding

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35. The magnitude of vecA vecB equals:

  1. the area of the parallelogram formed by vecA and vecB
  2. the perimeter of the parallelogram
  3. zero always
  4. the product of their magnitudes always

Answer: A) the area of the parallelogram formed by vecA and vecB

Explanation: vecA vecB = ABsintheta = base × height. SLO P-11-B-02 · Understanding

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36. hatj hatk =

  1. -hati
  2. 0
  3. 1
  4. hati

Answer: D) hati

Explanation: Using the cyclic order hati to hatj to hatk: hatj hatk = hati. SLO P-11-B-02 · Understanding

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37. If vecA vecB = 0 and neither vector is zero, the vectors are:

  1. anti-parallel
  2. perpendicular
  3. equal
  4. parallel

Answer: B) perpendicular

Explanation: costheta = 0 Rightarrow theta = 90^circ. SLO P-11-B-02 · Understanding

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38. vecA = 4, vecB = 5 and the angle between them is 60^circ. Then vecA vecB and vecA vecB are:

  1. 17.3 and 10
  2. 9 and 1
  3. 10 and 17.3
  4. 20 and 20

Answer: C) 10 and 17.3

Explanation: ABcostheta = 10; ABsintheta = 17.3. SLO P-11-B-02 · Understanding

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39. A force of 40 N acts at 30^circ to the x-axis. Its x- and y-components are:

  1. Fx = 20 N, Fy = 34.6 N
  2. Fx = 40 N, Fy = 40 N
  3. Fx = 17.3 N, Fy = 10 N
  4. Fx = 34.6 N, Fy = 20 N

Answer: D) Fx = 34.6 N, Fy = 20 N

Explanation: Fx = Fcostheta, Fy = Fsintheta: Fx = 34.6 N, Fy = 20 N. SLO P-11-B-01 · Understanding

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40. A vector has components Ax = 9 and Ay = 12. Its magnitude is:

  1. 15
  2. 3
  3. 225
  4. 21

Answer: A) 15

Explanation: vecA = Ax^2 + Ay^2 = 81 + 144 = 15. SLO P-11-B-01 · Understanding

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41. Work done is an example of:

  1. a vector product
  2. a vector quantity
  3. a scalar (dot) product, W = vecF vecd
  4. a product of magnitudes only

Answer: C) a scalar (dot) product, W = vecF vecd

Explanation: Work is Fdcostheta, a scalar. SLO P-11-B-02 · Understanding

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42. A force of 50 N acts at 60^circ to the x-axis. Its x- and y-components are:

  1. Fx = 50 N, Fy = 50 N
  2. Fx = 12.5 N, Fy = 21.7 N
  3. Fx = 43.3 N, Fy = 25 N
  4. Fx = 25 N, Fy = 43.3 N

Answer: D) Fx = 25 N, Fy = 43.3 N

Explanation: Fx = Fcostheta, Fy = Fsintheta: Fx = 25 N, Fy = 43.3 N. SLO P-11-B-01 · Understanding

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