• Amal Augustine
• December 11, 2025

Mastering Vector Applications in Motion: 30 Best & Advanced Physics MCQs With Solutions

Vector Applications in Motion ,mathematics forms the backbone of modern physics, especially when dealing with motion, forces, work, velocity, acceleration, and relative motion. From vector application in motion analysing how objects accelerate under applied force to understanding the motion of boats, bullets, raindrops, or vehicles, vectors allow us to describe physical quantities with both magnitude and direction.

Vector Applications in Motion 

Mastering Vector Applications in Motion strengthens problem-solving skills, enabling students to confidently approach complex NEET, JEE, and CUET numerical questions.Understanding vector applications in motion is essential for solving real-world physics problems, especially at the NEET, JEE, and CUET levels. Vectors allow us to represent motion with both magnitude and direction, making them powerful tools for analyzing displacement, velocity, acceleration, and force.

This curated set of Vector Applications in Motion MCQs is perfect for NEET, JEE, CUET, Olympiad, and Class 11–12 Physics learners who want to master advanced concepts like cross products, dot products, displacement vectors, average acceleration, projectile behaviour, and river-boat problems. Each vector applications in motion question includes all four options and the correct answer.

Important Vector Applications in Motion (MCQs With Answers)

1. When a force F = 6i − 18j + 10k acts on a body, it produces an acceleration of 8 m/s². The mass of the body is:

a) √115/4 kg
b) 10√2 kg
c) √115/2 kg
d) 115/2 kg
Answer: a

2. Vector A has magnitude 5 units in the xy-plane making 120° with +x. Vector B has magnitude 9 units along z. Find |A × B|:

a) 30
b) 35
c) 40
d) 45
Answer: d

3. If A = i + j and B = i + k, then A × B =

a) i + j + k
b) i − j + k
c) i + j − k
d) i − j − k
Answer: d

4. Displacement vector from A(0,3,−1) to B(−2,6,4) is:

a) −2i + 6j + 4k
b) −2i + 3j + 3k
c) −2i + 3j + 5k
d) 2i − 3j − 3k
Answer: c

5. A = 4i + 4j − 4k ; B = 3i + j + 4k. Angle between A & B:

a) 180°
b) 90°
c) 45°
d) 0°
Answer: b

6. Work done by force 4i + j + 3k when moving from (3,2,6) to (14,13,9):

a) 163
b) 64
c) 325
d) 48
Answer: b

7. Linear velocity for ω = (3i − 4j + k), r = (5i − 6j + 6k):

a) 6i − 2j + 3k
b) −18i − 13j + 2k
c) 18i + 13j + 2k
d) 6i − 2j + 8k
Answer: b

8. Displacement from A(2,2,3) → B(6,6,9):

a) 4i + 4j + 6k
b) 8i + 8j + 12k
c) 4i + 8j + 6k
d) 8i + 4j + 6k
Answer: a

9. Position r = (3ti − t²j + 4k). Magnitude of velocity at t = 5:

a) 3.55
b) 5.03
c) 8.75
d) 10.44
Answer: d

10. Velocity = i + j. Magnitude and direction:

a) 2 units, 45° with x-axis
b) 2 units, 30° with z-axis
c) √2 units, 45° with x-axis
d) √2 units, 60° with y-axis
Answer: c

11. A vector has components (4, 10). After rotation, x doubles. New y-component ≈

a) 20 m
b) 7.2 m
c) 5.0 m
d) 4.5 m
Answer: b

12. Initial velocity 3i + 4j, acceleration 0.4i + 0.3j. Speed after 10s:

a) 10
b) 7√2
c) 7
d) 8.5
Answer: b

13. For x = a cosωt, y = a sinωt, z = aωt, velocity magnitude:

a) √2 aω
b) 2aω
c) aω
d) √3 aω
Answer: a

14. r(t) = 15t² i + 4 − 20t j ; Acceleration at t=1:

a) 50
b) 100
c) 25
d) 40
Answer: a

15. A particle changes velocity from 5 m/s east to 5 m/s north in 10 s. Average acceleration:

a) 1/√2 m/s² NW
b) 1/2 m/s² NW
c) 1/√2 m/s² NE
d) 1/2 m/s² NE
Answer: a

16. Boat speed = 8 km/h, resultant = 10 km/h. River speed =

a) 4
b) 6
c) 8
d) 10
Answer: b

17. Curve not representing 1D motion:

a) Fig (a)
b) Fig (b)
c) Fig (c)
d) Fig (d)
Answer: c

18. Boat velocity = 3i + 4j. Water velocity = −3i − 4j. Relative velocity:

a) 5i + 6j
b) 6i + 8j
c) 6i + 8k
d) 5j − 6k
Answer: b

19. Boat speed = 13 km/h. Crosses 1 km river in 12 minutes. River speed =

a) 12
b) 10
c) 8
d) 6
Answer: a

20. Truck gun firing backward at 30° to vertical, muzzle = 4 m/s. Truck speed to make bullet vertical:

a) 1 m/s
b) √3 m/s
c) 0.5 m/s
d) 2 m/s
Answer: d

21. Swimmer speed = 0.5 m/s at 120°, water speed = ?

a) 1.0
b) 0.5
c) 0.25
d) 0.43
Answer: c

22. Raindrop radius 0.3 mm, terminal v = 1 m/s, viscosity = 8×10⁻⁵ poise. Viscous force =

a) 45.2×10⁻⁴
b) 101.73×10⁻⁵
c) 16.95×10⁻⁴
d) 16.95×10⁻⁵
Answer: a

23. Retardation = kx, distance covered before stopping:

a) v√k
b) v/√k
c) 2v/√k
d) None
Answer: b

24. Train east, car north, same speed. Relative direction of car to train:

a) East-north
b) West-north
c) South-east
d) None
Answer: b

25. Man crosses 320 m river in 4 min, swimmer speed = 5/3 river speed. River speed =

a) 30
b) 40
c) 50
d) 60
Answer: d

26. Cars A=120 km/h, B=50 km/h (given directions). Relative speed =

a) 70
b) 120
c) 130
d) 170
Answer: c

27. Rain 30 m/s vertical. Man cycles 10 m/s east→west. Angle with vertical:

a) tan⁻¹(1/3) West
b) tan⁻¹(3) West
c) tan⁻¹(1/3) East
d) tan⁻¹(3) East
Answer: a

28. Train 150 m north at 10 m/s. Parrot flies south at 5 m/s. Crossing time =

a) 12 s
b) 8 s
c) 15 s
d) 10 s
Answer: d

29. Minimum speed of roller coaster at loop top (r=10m):

a) 20 m/s
b) 10 m/s
c) 15 m/s
d) 25 m/s
Answer: b

30. Car velocity at top of semicircular hill radius 40 m for normal force zero:

a) 15 m/s
b) 20 m/s
c) 30 m/s
d) 40 m/s
Answer: b

Conclusion

Vector applications in motion ,mathematics offers a powerful way to understand real-world motion, whether it is the behaviour of a boat crossing a river, a raindrop falling through air, or the complex 3D motion of particles. These vector applications in motion MCQs combine vector algebra with kinematics, work-energy concepts, and relative motion, giving students a complete practice set vector applications in motion aligned with competitive exam patterns. Mastering these vector applications in motion problems builds analytical strength, accuracy, and confidence—helping learners excel in NEET, JEE, CUET, and board examinations.

In competitive exams like NEET, JEE, and CUET, questions on vector applications in motion consistently test logical reasoning, precision, and conceptual clarity. Developing strong vector skills not only enhances exam performance but also builds a strong foundation for engineering, physics, robotics, and navigation-based careers.