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Ultimate Vector Algebra Numericals Mastery: Concept-Driven MCQs on Direction, Magnitude, and Products

Vector algebra numericals  forms the mathematical backbone of physics, connecting geometry with real-world physical quantities such as force, velocity, torque, and momentum. Unlike scalars, vectors carry both magnitude and direction, making them essential for accurately describing motion and interactions in space. Mastery of vector algebra numericals helps students confidently solve problems involving perpendicular vectors, resultant forces, angular relationships, and vector products.

Strong conceptual understanding often comes from solving diverse vector algebra numericals. Every step of vector algebra numericals you solve brings you closer to conceptual mastery.

In competitive exams like NEET, JEE, and CUET, vector questions often test conceptual clarity rather than lengthy calculations. In vector algebra numericals,understanding dot product, cross product, unit vectors, components, and geometric interpretations is key to scoring well. This curated set of vector algebra numericals MCQs strengthens intuition while reinforcing exam-oriented problem-solving skills.

Table of Contents

Vector Algebra Numericals MCQs (With Options & Answers)

1. If →A ⟂ →B, →A = 5i + 7j − 3k and →B = 2ai + 2j − ck. The value of c is

a) −2
b) 8
c) −7
d) −8
Answer: d

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

a) 90°
b) 60°
c) 45°
d) 0°
Answer: a

3. The magnitude of the resultant of vectors of magnitudes a and b is always

a) Equal to (a + b)
b) Less than (a + b)
c) Greater than (a + b)
d) Not greater than (a + b)
Answer: d

4. If a unit vector is 0.5i + 0.8j + ck, the value of c is

a) 1
b) 0.11
c) 0.001
d) 0.39
Answer: b

5. The angle made by vector i + j with the x-axis is

a) 90°
b) 45°
c) 22.5°
d) 30°
Answer: b

6. Component of vector A = axi + ayj + azk along (i − j) is

a) (ax + ay + az)
b) (ax − ay)
c) (ax − ay)/2
d) (ax + ay + az)
Answer: c

7. For vectors A and B making angle θ, which relation is correct?

a) A × B = B × A
b) A × B = B × A sinθ
c) A × B = B × A
d) A × B = −B × A
Answer: d

8. Two vectors A = i − 2j − 3k and B = 4i − 2j + 6k. Angle made by A + B with x-axis is

a) 30°
b) 45°
c) 60°
d) 90°
Answer: b

9. Parallel vectors among the following are

a) A and B
b) B and C
c) A and D
d) C and D
Answer: b

10. A vector Q of magnitude 8 is added to vector P along x-axis. Resultant R lies along y-axis with magnitude 2P. Magnitude of P is

a) 6/5
b) 8/5
c) 12/5
d) 16/5
 Answer: b

11. Angle (in rad) made by vector 3i + j with x-axis is

a) π/6
b) π/4
c) π/3
d) π/2
Answer: a

12. Pressure is a scalar quantity because

a) Force and area are vectors
b) It is magnitude of force per area
c) It depends on normal component of force
d) It depends on area size
Answer: c

13. Which is NOT a vector quantity?

a) Weight
b) Nuclear spin
c) Momentum
d) Potential energy
Answer: d

14. Two equal forces P act at 120°. Resultant magnitude is

a) P/2
b) P/4
c) P
d) 2P
Answer: c

15. If A·B = 0 and A·C = 0, A is parallel to

a) C
b) B
c) B × C
d) B·C
Answer: c

16. Resultant of perpendicular forces 3 N and 4 N is

a) 5 N
b) 7 N
c) 20 N
d) 0
 Answer: a

17. If |A·B| = |A×B|, the angle between vectors is

a) 45°
b) 90°
c) 180°
d) 360°

Answer: a

18. Unit vector along A is

a) A → A
b) A·A
c) A × A
d) A / |A|
Answer: d

19. Velocity is a

a) Scalar
b) Vector
c) Neither
d) Both
✅ Answer: b

20. If sum of two vectors is perpendicular to their difference, then

a) A = B
b) A = 2B
c) B = 2A
d) Same direction
Answer: a

21. Torque of force F = 3i + 7j + 4k about origin when applied at r = 2i + j + 2k is

a) i + 5j − 8k
b) i + j + k
c) i + j
d) 3i + 2j + 3k
Answer: a

22. Scalar product of A = 2i + j − k and B = −j + k is

a) 3
b) 4
c) −4
d) −3
 Answer: d

23. If r = 2i + j, velocity vector is

a) 2i + 2j
b) 2i + j
c) i + j
d) Zero
Answer: a

24. Two equal forces P act at right angles. Third force cancels them along bisector. Magnitude is

a) P
b) 2P
c) √2P
d) 2√2P
Answer: c

25. The vector sum of two forces is perpendicular to their vector difference. In that case, the forces

a) are not equal to each other in magnitude
b) cannot be predicted
c) are equal to each other
d) are equal to each other in magnitude
Answer: d

26. The sum of two vectors A and B is at right angles to their difference. This is possible if

a) A = 2B
b) A = B
c) A = 3B
d) B = 2A
✅ Answer: b

27. What is the torque of a force

F = 3i + 7j + 4k
about the origin, if it acts on a particle at position vector
r = 2i + j + 2k?

a) i + 5j − 8k
b) i + j + k
c) i + j
d) 3i + 2j + 3k
✅ Answer: a

28. The scalar product of two vectors

A = 2i + j − k and B = −j + k is

a) 3
b) 4
c) −4
d) −3
Answer: d

29. The velocity vector of the motion described by the position vector

r = 2i + j is

a) 2i + 2j
b) 2i + j
c) i + j
d) Zero
Answer: a

30. Two forces each of magnitude P act at right angles. Their effect is neutralized by a third force acting along their bisector in the opposite direction. The magnitude of the third force is

a) P
b) 2P
c) √2P
d) 2√2P
Answer: c

vector algebra numericals

Conclusion

Vector algebra numericals strengthen the foundation of physics by connecting abstract mathematics with physical reality. Through problems in vector algebra numericals on dot product, cross product, torque, unit vectors, and angular relationships, students develop spatial reasoning and analytical clarity. These vector algebra numericals MCQs reinforce conceptual understanding while improving exam accuracy and speed. Consistent practice of vector algebra numericals ensures confidence in mechanics, electromagnetism, and advanced physics topics. Mastery of vectors is not just exam preparation—it is a gateway to understanding the language of physics itself.With regular exposure to diverse vector algebra numericals, students develop precision, conceptual strength, and the strategic thinking required for top-tier exam performance.

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