Vector Addition — JEE Main Physics MCQs with Solutions
Free JEE Main Physics Vector Addition MCQs with step-by-step solutions (11 questions). Part of Vectors. Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Vector Addition · medium · numerical
Two forces of 3 N and 4 N act at right angles. Their resultant is:
A. 1 N
B. 7 N
C. 12 N
D. 5 N ✓ Correct
Solution: R = √(3²+4²) = 5 N.
Q2 — Vector Addition · hard · numerical
Two equal vectors of magnitude 10 units act at 120° to each other. Their resultant is:
A. 10 units ✓ Correct
B. 0
C. 20 units
D. 10√3 units
Solution: R = √(A²+A²+2A²cos120°) = √(100+100−100) = 10 units.
Q3 — Vector Addition · medium · numerical
Two vectors of magnitudes 8 and 6 give a maximum resultant of:
A. 10
B. 14 ✓ Correct
C. 2
D. 48
Solution: Maximum when parallel: 8 + 6 = 14.
Q4 — Vector Addition · medium · numerical
Two forces of 5 N and 12 N act at right angles. The resultant magnitude is:
A. 7 N
B. 13 N ✓ Correct
C. 17 N
D. 60 N
Solution: R = √(5²+12²) = 13 N.
Q5 — Vector Addition · hard · numerical
Two vectors of 10 units each act at 60°. Their resultant is:
A. 10√3 units ✓ Correct
B. 0
C. 10 units
D. 20 units
Solution: R = √(100+100+2(100)(0.5)) = √300 = 10√3 units.
Q6 — Vector Addition · medium · numerical
The minimum resultant of two vectors of magnitude 7 and 4 is:
A. 0
B. 11
C. 28
D. 3 ✓ Correct
Solution: Minimum when antiparallel: 7 − 4 = 3.
Q7 — Vector Addition · hard · numerical
The resultant of two vectors P and Q is R. When Q is doubled, the new resultant is perpendicular to P. Then R equals:
A. 2Q
B. P
C. P + Q
D. Q ✓ Correct
Solution: Perpendicularity gives P + 2Q cosθ = 0 ⇒ cosθ = −P/2Q. Then R² = P² + Q² + 2PQcosθ = P² + Q² − P² = Q² ⇒ R = Q — a classic identity.
Q8 — Vector Addition · hard · numerical
Two forces P + Q and P − Q act at right angles to each other. The magnitude of their resultant is:
A. √(2P² + 2Q²) ✓ Correct
B. P + Q
C. 2P
D. √(P² + Q²)
Solution: R² = (P+Q)² + (P−Q)² = 2P² + 2Q².
Q9 — Vector Addition · hard · numerical
The resultant of two equal vectors of magnitude A is also of magnitude A. The angle between the two vectors is:
A. 45°
B. 90°
C. 120° ✓ Correct
D. 60°
Solution: A² = A² + A² + 2A²cosθ ⇒ cosθ = −1/2 ⇒ θ = 120°.
Q10 — Vector Addition · hard · numerical
Vectors A and B satisfy |A + B| = |A − B|. The angle between A and B is:
A. 180°
B. 90° ✓ Correct
C. 0°
D. 45°
Solution: Squaring both: 2A·B = −2A·B ⇒ A·B = 0 ⇒ perpendicular.
Q11 — Vector Addition · hard · numerical
The maximum and minimum resultants of two forces are in the ratio 3 : 1. The forces are in the ratio:
A. 4 : 3
B. 9 : 1
C. 3 : 1
D. 2 : 1 ✓ Correct
Solution: (P+Q)/(P−Q) = 3 ⇒ P + Q = 3P − 3Q ⇒ 4Q = 2P ⇒ P : Q = 2 : 1.