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 · theory
Two vectors have magnitudes $6$ and $8$ units. Their resultant has magnitude $10$ units. The angle between them is
A. $0^\circ$
B. $60^\circ$
C. $90^\circ$ ✓ Correct
D. $120^\circ$
Solution: Check with $R^2 = A^2 + B^2 + 2AB\cos\theta$: here $10^2 = 6^2 + 8^2$, i.e. $100 = 36 + 64$, so $2AB\cos\theta = 0 \Rightarrow \theta = 90^\circ$. (A 6-8-10 triangle is right-angled.)
Q2 — Vector Addition · medium · numerical
Two vectors each of magnitude $5$ units act at an angle of $120^\circ$. Their resultant is
A. $10$
B. $5$ ✓ Correct
C. $5\sqrt3$
D. $0$
Solution: $R = \sqrt{5^2 + 5^2 + 2\cdot5\cdot5\cos120^\circ} = \sqrt{25 + 25 - 25} = \sqrt{25} = 5$ units.
Q3 — Vector Addition · medium · theory
Two vectors have equal magnitudes. Their resultant is equal to either vector. The angle between them is
A. $30^\circ$
B. $60^\circ$
C. $90^\circ$
D. $120^\circ$ ✓ Correct
Solution: With $|A|=|B|=a$ and $R=a$: $a^2 = 2a^2(1+\cos\theta) \Rightarrow \cos\theta = -\tfrac{1}{2} \Rightarrow \theta = 120^\circ$.
Q4 — Vector Addition · medium · numerical
Two vectors have magnitudes $3$ and $4$ units. Which of the following cannot be the magnitude of their resultant?
A. $1$
B. $5$
C. $8$ ✓ Correct
D. $7$
Solution: The resultant must lie between $|4-3| = 1$ and $4+3 = 7$. A value of $8$ is outside this range, so it is impossible.
Q5 — Vector Addition · medium · theory
If $|\vec A+\vec B| = |\vec A-\vec B|$, then
A. Vectors are parallel
B. Vectors are perpendicular ✓ Correct
C. Magnitudes are equal
D. One vector is zero
Solution: Squaring both sides: $A^2+B^2+2\vec A\cdot\vec B = A^2+B^2-2\vec A\cdot\vec B \Rightarrow \vec A\cdot\vec B = 0$, so the vectors are perpendicular.
Q6 — 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.
Q7 — 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.
Q8 — 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.
Q9 — 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.
Q10 — 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.
Q11 — 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.