1. Component of A along B when A = 2i + 3j and B = i + j

a) 1/√2
b) 3/√2
c) 5/√2
d) 7/√2
 Answer: c

2. If C = A × B and D = B × A, angle between C and D is

a) 30°
b) 90°
c) 180°
d) 0°
 Answer: d

3. Angle made by A = 4i + 3j + 12k with x-axis

a) sin⁻¹(3/13)
b) cos⁻¹(4/13)
c) sin⁻¹(4/13)
d) cos⁻¹(3/13)
Answer: c

4. Which of the following is a vector quantity?

a) Temperature
b) Flux density
c) Magnetic field intensity
d) Time
Answer: c

5. If a₁ and a₂ are non-collinear unit vectors and |a₁ + a₂| = √3, then (a₁ – a₂)·(2a₁ + a₂)

a) 2
b) √3
c) 1/2
d) a₁ and a₂
 Answer: c

6. Two vectors are perpendicular if

a) A·B = 1
b) A × B = 0
c) A = 0
d) A × B = A
 Answer: c

7. A particle moves from (0,0) to (3,3). Angle with x-axis is

a) 30°
b) 45°
c) 60°
d) 0°
 Answer: d

8. Torque of F = −3i + 2j + k at r = 8i + 2j + 3k

a) 14i − 38j + 16k
b) 4i + 4j + 6k
c) −14i + 38j − 16k
d) −4i + 17j + 22k
 Answer: a

9. Work done by F = 5i + 3j + 4k when displacement is s = 6i − 5k

a) 10
b) 12√5
c) 5√122
d) 20
 Answer: c

10. Dot product of displacement after 10 cm (x-axis) and 20 cm (y-axis) with a 2 cm vector at 45°

a) 30 cm
b) 30√2 cm
c) 30/√2 cm
d) 15 cm
 Answer: a

11. Vector A = 4i + 7j. Angle with y-axis

a) cos⁻¹(7/√11)
b) cos⁻¹(4/√11)
c) cos⁻¹(7/√65)
d) cos⁻¹(4/√65)
 Answer: c

12. Unit vector along a + b where a = i + 2j + 2k and b = i − j + k

a) (2i + j + 3k)/√14
b) (2i − j + 4k)/√20
c) (2i + j + 3k)/√13
d) (2i + j − 3k)/√10
Answer: a

13. Component of P = 2i + 3j along Q = i + j

a) 2
b) 2√5
c) 5/√2
d) √2/5
Answer: c

14. If y-component of A is 3 m and A makes 30° with positive y-axis, magnitude of A

a) 2√3
b) √11
c) √15
d) √21
Answer: a

15. If |A + B| = |A − B|, angle between A and B is

a) 45°
b) 90°
c) 180°
d) 0°
Answer: a

16. If A × B = 3(A·B), θ equals

a) 60°
b) 30°
c) 90°
d) 45°
 Answer: a

17. If |A × B| = 3(A·B), then |A + B|

a) √(A² + B² + AB)
b) √(A² + B² + AB/3)
c) A + B
d) √(A² + B² + 3AB)
Answer: a

18. If vector (2i + 3j + 8k) is perpendicular to (4i − 4j + k), value is

a) −1
b) 1/2
c) −1/2
d) 1
 Answer: c

19. For unit vector 0.5i + 0.8j + ck, the value of c is

a) 1
b) 0.11
c) 0.01
d) 0.39
 Answer: b

20. Which is NOT a vector quantity?

a) Speed
b) Velocity
c) Torque
d) Displacement
 Answer: a

21. A⋅(B × A) equals

a) A²B
b) 0
c) A²B sinθ
d) A²B cosθ
 Answer: b

22. Component of A = 2i + 3j − k along B = i + 2j + 2k

a) 1
b) 5
c) 2
d) 6
 Answer: c

23. For any non-zero vector A

a) A·A = 0
b) A × A < 0
c) A × A = 0
d) A × A > 0
 Answer: c

24. Matching List question

a) (A→iv), (B→i), (C→iii), (D→ii)
b) (A→iv), (B→iii), (C→i), (D→ii)
c) (A→iii), (B→ii), (C→iv), (D→i)
d) (A→i), (B→iv), (C→ii), (D→iii)
 Answer: b

25. If A·B = |A × B|, then |A − B| =

a) √(A² + B²)
b) √(A² + B² + √2AB)
c) √(A² + B² + 2AB)
d) √(A² + B² − √2AB)
 Answer: d

26. If P × Q = Q × P, angle between them is

a) 180°
b) 120°
c) 90°
d) 100°
 Answer: a

27. In a cube of side a, vector from center of face ABOD to BEFO

a) ½a(i − k)
b) ½a(j − i)
c) ½a(j − k)
d) ½a(k − i)
Answer: b

28. If A × B = B × A, angle between A and B is

a) π
b) π/3
c) π/2
d) π/4
 Answer: a

29. Dot product of A = (i + j + k) with unit vector parallel to (i − j + k)

a) 1/√3
b) 2/√3
c) √3
d) 3
 Answer: a

30. Which statement is NOT true?

a) (A·A)(B·C) is a scalar
b) (A × B)·(B × C) is a scalar
c) (A × C) × (B × C) is a scalar
d) A × (B × C) is a vector
 Answer: c

Conclusion

These 30 vector operations MCQs strengthen your understanding of components, projections, dot and cross products, torque, unit vectors, and vector geometry. Mastering these vector operations mcqs concepts builds a strong foundation for NEET, JEE Main, JEE Advanced, CUET, and Class 11–12 Physics. Regular practice of vector operations MCQs such mixed-difficulty questions ensures faster problem-solving and higher exam confidence.

Ultimately, consistent practice with vector operations MCQs , mechanics questions builds problem-solving stamina and enhances conceptual retention. Students who regularly engage with these vector operations mcqs become faster and more accurate, gaining a competitive edge in exams. Keep revisiting these vector operations mcqs problems, analyse your mistakes, and strengthen your physics reasoning one vector at a time.