NUST NET Maths chapter 11: Maths · Vectors MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

14 exam-style questions on Maths · Vectors, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

14 questions · 1 topics · 10 per test

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What chapter 11 covers

Ten Maths · Vectors questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A vector makes an angle of 60° with the x-axis and 60° with the y-axis. The acute angle it makes with the z-axis is

  1. A
    60°
  2. B
    30°
  3. C
    90°
  4. D
    45°
Show answer

Answer: D. cos2 α + cos2 β + cos2 γ = 1 gives 1/4 + 1/4 + cos2 γ = 1, so cos γ = 1/√2 and γ = 45°.

2. The area of the triangle with adjacent sides a = i + j − k and b = i − j + k is (in square units)

  1. A
    2√2
  2. B
    √2
  3. C
    2
  4. D
    1
Show answer

Answer: B. a × b = −2j − 2k, whose magnitude is 2√2. The triangle is half the parallelogram, so its area is √2; 2√2 is the parallelogram.

3. The direction cosines of the vector 2i − j + 2k are

  1. A
    2, −1, 2
  2. B
    2/3, −1/3, 2/3
  3. C
    2/9, −1/9, 2/9
  4. D
    2/3, 1/3, 2/3
Show answer

Answer: B. Divide each component by the magnitude √(4 + 1 + 4) = 3: 2/3, −1/3, 2/3. The numbers 2, −1, 2 are direction ratios, not direction cosines.

4. A force F = 2i + j + 3k moves a particle from A(1, 0, 2) to B(3, 4, 1). The work done is

  1. A
    11 units
  2. B
    13 units
  3. C
    5 units
  4. D
    −5 units
Show answer

Answer: C. Displacement = B − A = 2i + 4j − k, so W = F·d = 4 + 4 − 3 = 5 units. Using the position vector of B instead of the displacement gives 13.

5. The projection of a = 2i + 3j − k on b = i + 2j + 2k is

  1. A
    6
  2. B
    2/3
  3. C
    6/√14
  4. D
    2
Show answer

Answer: D. Projection of a on b = (a·b)/|b| = (2 + 6 − 2)/3 = 2. Dividing by |a| = √14 instead gives the projection of b on a.

6. If a = i + 2j and b = j − k, then a × b equals

  1. A
    2i − j − k
  2. B
    −2i − j + k
  3. C
    −2i + j + k
  4. D
    2i + j + k
Show answer

Answer: C. Expand the determinant with rows (1, 2, 0) and (0, 1, −1): i(−2 − 0) − j(−1 − 0) + k(1 − 0) = −2i + j + k. 2i − j − k is b × a.

7. The vectors i + 2j + 3k, 2i + λj + k and 3i + j + 4k are coplanar when λ equals

  1. A
    1
  2. B
    −1
  3. C
    5
  4. D
    −5
Show answer

Answer: B. Coplanar vectors have a zero scalar triple product: 1(4λ − 1) − 2(8 − 3) + 3(2 − 3λ) = −5λ − 5 = 0, so λ = −1.

8. The vectors 2i + λj − k and 3i − 2j + 4k are perpendicular when λ equals

  1. A
    −1
  2. B
    5
  3. C
    1
  4. D
    −5
Show answer

Answer: C. Perpendicular vectors have a zero dot product: 6 − 2λ − 4 = 0, so λ = 1. Treating (−1)(4) as +4 gives λ = 5.

9. If |a| = 2, |b| = 3 and the angle between a and b is 60°, then |a − b| equals

  1. A
    √19
  2. B
    √7
  3. C
    1
  4. D
    √13
Show answer

Answer: B. |a − b|2 = |a|2 + |b|2 − 2a·b = 4 + 9 − 2(2)(3)(1/2) = 7, so |a − b| = √7. √19 is |a + b|.

10. The angle between a = i + j and b = j + k is

  1. A
    60°
  2. B
    45°
  3. C
    90°
  4. D
    30°
Show answer

Answer: A. a·b = 0 + 1 + 0 = 1 and |a||b| = √2 × √2 = 2, so cos θ = 1/2 and θ = 60°.

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Ways to practise this chapter

Maths · Vectors: questions students ask

How many Maths · Vectors MCQs are there?

14, each with the answer and a short explanation, across 1 topics: Vectors in space. Every chapter test draws ten of them, so you can take it many times.

Is the NUST NET Maths chapter 11 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

Can I read the explanations in Urdu?

Yes. In practice mode and on your results you can switch the explanations to Urdu.

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