MCQs / Physics / Vectors

Vectors MCQs — Physics

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.

1. The components of a vector are always:

  1. perpendicular to each other (for rectangular components)
  2. equal in size
  3. larger than the vector
  4. parallel to each other

Answer: A) perpendicular to each other (for rectangular components)

Explanation: Rectangular components lie along perpendicular axes. SLO P-11-B-01 · Understanding

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2. hati hatj =

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

Answer: A) hatk

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

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3. A vector of magnitude 10 units makes 90^circ with the x-axis. Its x-component is:

  1. 5
  2. -10
  3. 10
  4. 0

Answer: D) 0

Explanation: 10cos 90^circ = 0; the vector lies along the y-axis. SLO P-11-B-01 · Understanding

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

  1. 6
  2. 1
  3. 2
  4. 0

Answer: D) 0

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

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5. A vector has components Ax = -3, Ay = -4. The angle it makes with the positive x-axis is:

  1. 126.9^circ
  2. 233.1^circ
  3. 53.13^circ
  4. 323.1^circ

Answer: B) 233.1^circ

Explanation: tantheta = AyAx; with the signs of the components the vector is in the correct quadrant, so theta = 233.1^circ. SLO P-11-B-01 · Understanding

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6. A force of 80 N acts at 53.13^circ to the x-axis. Its x- and y-components are:

  1. Fx = 80 N, Fy = 80 N
  2. Fx = 48 N, Fy = 64 N
  3. Fx = 64 N, Fy = 48 N
  4. Fx = 24 N, Fy = 32 N

Answer: B) Fx = 48 N, Fy = 64 N

Explanation: cos 53.13^circ = 0.6 and sin 53.13^circ = 0.8: Fx = 48 N, Fy = 64 N. SLO P-11-B-01 · Understanding

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7. If vecA vecB = vecA vecB, the angle between the vectors is:

  1. 60^circ
  2. 90^circ
  3. 45^circ
  4. 0^circ

Answer: C) 45^circ

Explanation: sintheta = costheta Rightarrow theta = 45^circ. SLO P-11-B-02 · Understanding

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8. hati hati =

  1. 0
  2. 1
  3. hati
  4. hatk

Answer: A) 0

Explanation: The cross product of parallel vectors is zero (sin 0^circ = 0). SLO P-11-B-02 · Understanding

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9. A vector has components Ax = 5 and Ay = 12. Its magnitude is:

  1. 13
  2. 7
  3. 17
  4. 169

Answer: A) 13

Explanation: vecA = Ax^2 + Ay^2 = 25 + 144 = 13. SLO P-11-B-01 · Understanding

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10. A force of 100 N acts at 45^circ to the x-axis. Its x- and y-components are:

  1. Fx = 70.7 N, Fy = 70.7 N
  2. Fx = 50 N, Fy = 50 N
  3. Fx = 100 N, Fy = 0 N
  4. Fx = 141 N, Fy = 141 N

Answer: A) Fx = 70.7 N, Fy = 70.7 N

Explanation: Fx = Fcostheta, Fy = Fsintheta: Fx = 70.7 N, Fy = 70.7 N. SLO P-11-B-01 · Understanding

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11. A vector has components Ax = 7 and Ay = -24. Its magnitude is:

  1. 26
  2. 625
  3. 25
  4. 31

Answer: C) 25

Explanation: vecA = Ax^2 + Ay^2 = 49 + 576 = 25. SLO P-11-B-01 · Understanding

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12. hati hati =

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

Answer: A) 1

Explanation: hatihaticos 0^circ = 1. SLO P-11-B-02 · Understanding

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

  1. 2
  2. 8
  3. 1
  4. 0

Answer: D) 0

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

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14. A vector has components Ax = 3, Ay = 4. The angle it makes with the positive x-axis is:

  1. 143.1^circ
  2. 53.13^circ
  3. 233.1^circ
  4. 36.87^circ

Answer: B) 53.13^circ

Explanation: tantheta = AyAx; with the signs of the components the vector is in the correct quadrant, so theta = 53.13^circ. SLO P-11-B-01 · Understanding

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15. A boat heads north at 4 m/s in a river flowing east at 3 m/s. Its resultant speed is:

  1. 1 m/s
  2. 5 m/s
  3. 7 m/s
  4. 3.5 m/s

Answer: B) 5 m/s

Explanation: 4^2 + 3^2 = 5 m/s. SLO P-11-B-01 · Understanding

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16. vecA = 8, vecB = 3 and the angle between them is 90^circ. Then vecA vecB and vecA vecB are:

  1. 1.47 10^-15 and 24
  2. 12 and 12
  3. 11 and 5
  4. 24 and 1.47 10^-15

Answer: A) 1.47 10^-15 and 24

Explanation: ABcostheta = 1.47 10^-15; ABsintheta = 24. SLO P-11-B-02 · Understanding

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17. Torque is an example of:

  1. a scalar product
  2. a vector (cross) product, vectau = vecr vecF
  3. a scalar quantity
  4. an addition of vectors

Answer: B) a vector (cross) product, vectau = vecr vecF

Explanation: Torque has a direction given by the right-hand rule. SLO P-11-B-02 · Understanding

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18. Two forces vecA = 3hati + 2hatj N and vecB = 1hati + 4hatj N act together. The resultant is:

  1. 3hati + 8hatj N
  2. 4hati + 6hatj N
  3. 2hati - 2hatj N
  4. 4hati + 2hatj N

Answer: B) 4hati + 6hatj N

Explanation: Add the components separately. SLO P-11-B-01 · Understanding

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19. A force vecF = 3hati + 4hatj N moves a body through vecd = 2hati + 1hatj m. The work done is:

  1. 14 J
  2. 5 J
  3. 11 J
  4. 10 J

Answer: D) 10 J

Explanation: W = (3)(2) + (4)(1) = 10 J. SLO P-11-B-02 · Understanding

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

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

Answer: A) -3

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

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21. A vector has components Ax = 3 and Ay = 4. Its magnitude is:

  1. 1
  2. 5
  3. 25
  4. 7

Answer: B) 5

Explanation: vecA = Ax^2 + Ay^2 = 9 + 16 = 5. SLO P-11-B-01 · Understanding

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22. hatk hati =

  1. 1
  2. 0
  3. hatj
  4. -hatj

Answer: C) hatj

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

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23. Which property is true?

  1. vecA vecB = -vecB vecA
  2. vecA vecB = -vecB vecA
  3. vecA vecA = 0
  4. vecA vecB = vecB vecA

Answer: A) vecA vecB = -vecB vecA

Explanation: The cross product is anti-commutative; the dot product is commutative. SLO P-11-B-02 · Understanding

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24. vecA = 6, vecB = 10 and the angle between them is 30^circ. Then vecA vecB and vecA vecB are:

  1. 30 and 52
  2. 60 and 60
  3. 16 and 4
  4. 52 and 30

Answer: D) 52 and 30

Explanation: ABcostheta = 52; ABsintheta = 30. SLO P-11-B-02 · Understanding

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25. vecA = 5, vecB = 5 and the angle between them is 0^circ. Then vecA vecB and vecA vecB are:

  1. 25 and 0
  2. 10 and 0
  3. 12.5 and 12.5
  4. 0 and 25

Answer: A) 25 and 0

Explanation: ABcostheta = 25; ABsintheta = 0. SLO P-11-B-02 · Understanding

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