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Vectors — NEET Physics MCQs with Solutions
Free NEET Physics Vectors MCQs with step-by-step solutions covering Vector Addition, Vector Subtraction, Vector Multiplication, Area and Volume, Mixed Type, Direction Cosine. Practise online on Prepizo — no login needed.
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Sample questions with solutions
Q1 — Vector Addition · easy · numerical
Two forces of 3 N and 4 N act on a body at right angles to each other. The magnitude of their resultant is:
A. 5 N ✓ Correct
B. 7 N
C. 1 N
D. 12 N
Solution: For perpendicular vectors, R = √(A² + B²) = √(3² + 4²) = √25 = 5 N.
Q2 — Vector Addition · easy · numerical
Two vectors, each of magnitude 5 units, give a resultant of magnitude 5√2 units. The angle between them is:
A. 90° ✓ Correct
B. 45°
C. 60°
D. 120°
Solution: (5√2)² = 5² + 5² + 2·5·5·cosθ ⇒ 50 = 50 + 50cosθ ⇒ cosθ = 0 ⇒ θ = 90°.
Q3 — Vector Addition · easy · numerical
Two vectors of magnitudes 3 units and 4 units have a resultant of magnitude 5 units. The angle between them is:
A. 90° ✓ Correct
B. 0°
C. 180°
D. 45°
Solution: 5² = 3² + 4² + 2·3·4·cosθ ⇒ 25 = 25 + 24cosθ ⇒ cosθ = 0 ⇒ θ = 90°.
Q4 — Vector Addition · easy · numerical
A vector of magnitude 10 units makes an angle of 30° with the x-axis. Its x and y components are:
A. (5√3, 5) ✓ Correct
B. (5, 5√3)
C. (5√2, 5√2)
D. (10, 0)
Solution: Ax = 10·cos30° = 10·(√3/2) = 5√3; Ay = 10·sin30° = 10·(1/2) = 5.
Q5 — Vector Addition · easy · theory
The unit vector along $\vec A + \vec B$, where $\vec A = \hat{i} + \hat{j}$ and $\vec B = \hat{i} - \hat{j}$, is
A. $\hat{k}$
B. $\hat{i}$ ✓ Correct
C. $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
D. $\hat{j}$
Solution: $\vec A + \vec B = 2\hat{i}$. The unit vector is $\frac{2\hat{i}}{2} = \hat{i}$.
Q6 — Vector Subtraction · easy · numerical
Two vectors each of magnitude $5$ units are inclined at $60^\circ$. The magnitude of their difference is
A. $5$ ✓ Correct
B. $5\sqrt{2}$
C. $5\sqrt{3}$
D. $10$
Solution: $|\vec A - \vec B| = 2(5)\sin(60^\circ/2) = 10\sin 30^\circ = 5$ units.
Q7 — Vector Subtraction · easy · numerical
Two vectors have magnitudes $7$ and $4$ units. Which of the following CANNOT be the magnitude of $\vec A - \vec B$?
A. $11$
B. $2$ ✓ Correct
C. $7$
D. $3$
Solution: The difference must lie between $3$ and $11$; a value of $2$ is impossible.
Q8 — Vector Subtraction · easy · theory
A cyclist rides along a circular track at constant speed $v$. After turning through $60^\circ$ of arc, the magnitude of the change in velocity is
A. $2v$
B. $v$ ✓ Correct
C. $v\sqrt{3}$
D. $v/2$
Solution: $|\Delta\vec v| = 2v\sin(\theta/2) = 2v\sin 30^\circ = v$.
Q9 — Vector Multiplication · easy · numerical
If $\vec A = 2\hat{i} + 3\hat{j}$ and $\vec B = \hat{i} - \hat{j}$, then $\vec A \cdot \vec B$ is
A. $1$
B. $-1$ ✓ Correct
C. $5$
D. $-5$
Solution: $\vec A\cdot\vec B = (2)(1) + (3)(-1) = 2 - 3 = -1$.
Q10 — Vector Multiplication · easy · numerical
A force $\vec F = (3\hat{i} + 4\hat{j})$ N displaces a body by $\vec d = (2\hat{i} + \hat{j})$ m. The work done is
A. $10$ J ✓ Correct
B. $11$ J
C. $14$ J
D. $5$ J
Solution: $W = \vec F\cdot\vec d = (3)(2) + (4)(1) = 10$ J.
Q11 — Vector Multiplication · easy · numerical
$\hat{i}\cdot(\hat{j}\times\hat{k})$ equals
A. $0$
B. $\hat{i}$
C. $-1$
D. $1$ ✓ Correct
Solution: $\hat{j}\times\hat{k} = \hat{i}$, and $\hat{i}\cdot\hat{i} = 1$.
Q12 — Vector Multiplication · easy · numerical
If $|\vec A| = 4$, $|\vec B| = 3$ and the angle between them is $30^\circ$, then $|\vec A \times \vec B|$ is
A. $6\sqrt{3}$
B. $3$
C. $6$ ✓ Correct
D. $12$
Solution: $|\vec A\times\vec B| = AB\sin\theta = 4\times 3\times\tfrac{1}{2} = 6$.
Q13 — Vector Multiplication · easy · numerical
If $|\vec A| = 4$, $|\vec B| = 3$ and the angle between them is $60^\circ$, then $\vec A \cdot \vec B$ is
A. $6\sqrt{3}$
B. $6$ ✓ Correct
C. $4$
D. $12$
Solution: $\vec A\cdot\vec B = AB\cos\theta = 4\times 3\times\tfrac{1}{2} = 6$.
Q14 — Vector Multiplication · easy · theory
If $\vec A \cdot \vec B = |\vec A \times \vec B|$, the angle between $\vec A$ and $\vec B$ is
A. $30^\circ$
B. $60^\circ$
C. $45^\circ$ ✓ Correct
D. $90^\circ$
Solution: $AB\cos\theta = AB\sin\theta \Rightarrow \tan\theta = 1 \Rightarrow \theta = 45^\circ$.
Q15 — Vector Multiplication · easy · numerical
If $|\vec A| = 5$ and $|\vec B| = 3$, then $(\vec A + \vec B)\cdot(\vec A - \vec B)$ equals
A. $-16$
B. $16$ ✓ Correct
C. $8$
D. $34$
Solution: $(\vec A+\vec B)\cdot(\vec A-\vec B) = A^2 - B^2 = 25 - 9 = 16$.
Q16 — Vector Multiplication · easy · theory
$(\vec A \times \vec B)^2 + (\vec A \cdot \vec B)^2$ equals
A. $2A^2B^2$
B. $A^2 + B^2$
C. $(A+B)^2$
D. $A^2B^2$ ✓ Correct
Solution: $A^2B^2\sin^2\theta + A^2B^2\cos^2\theta = A^2B^2(\sin^2\theta + \cos^2\theta) = A^2B^2$.
Q17 — Vector Multiplication · easy · theory
A unit vector perpendicular to both $\hat{i}$ and $\hat{j}$ is
A. $\hat{k}$ ✓ Correct
B. $\hat{i}$
C. $\hat{i}+\hat{j}+\hat{k}$
D. $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$
Solution: $\hat{i}\times\hat{j} = \hat{k}$, which is perpendicular to both ($-\hat{k}$ also works).
Q18 — Vector Multiplication · easy · numerical
A force $\vec F = (2\hat{i} + 3\hat{j})$ N acts on a body moving with velocity $\vec v = (\hat{i} + 2\hat{j})$ m/s. The power delivered is
A. $5$ W
B. $7$ W
C. $8$ W ✓ Correct
D. $4$ W
Solution: $P = \vec F\cdot\vec v = (2)(1) + (3)(2) = 8$ W.
Q19 — Vector Multiplication · easy · theory
If $\vec A \cdot \vec B = -|\vec A||\vec B|$, the angle between the vectors is
A. $45^\circ$
B. $0^\circ$
C. $180^\circ$ ✓ Correct
D. $90^\circ$
Solution: $\cos\theta = -1 \Rightarrow \theta = 180^\circ$ (antiparallel vectors).
Q20 — Vector Multiplication · easy · theory
If $\hat{a}$ and $\hat{b}$ are unit vectors with $\hat{a}\cdot\hat{b} = 1$, then
A. They are opposite
B. They are perpendicular
C. They point in the same direction ✓ Correct
D. Nothing can be said
Solution: $\hat{a}\cdot\hat{b} = \cos\theta = 1 \Rightarrow \theta = 0^\circ$: identical directions.
Q21 — Area and Volume · easy · theory
The area of a parallelogram with sides of lengths $5$ and $4$ units inclined at $30^\circ$ is
A. $10$ sq units ✓ Correct
B. $20$ sq units
C. $5$ sq units
D. $10\sqrt{3}$ sq units
Solution: Area $= ab\sin\theta = 5\times4\times\sin 30^\circ = 10$ sq units.
Q22 — Area and Volume · easy · theory
The area of the triangle whose two sides are the vectors $3\hat{i}$ and $4\hat{j}$ is
A. $3$ sq units
B. $24$ sq units
C. $6$ sq units ✓ Correct
D. $12$ sq units
Solution: Area $= \tfrac{1}{2}|\vec A\times\vec B| = \tfrac{1}{2}(3)(4)\sin 90^\circ = 6$ sq units.
Q23 — Area and Volume · easy · theory
The diagonals of a parallelogram are $2\hat{i}$ and $4\hat{j}$. Its area is
A. $4$ sq units ✓ Correct
B. $2$ sq units
C. $8$ sq units
D. $16$ sq units
Solution: Area $= \tfrac{1}{2}|\vec d_1\times\vec d_2| = \tfrac{1}{2}(2)(4) = 4$ sq units.
Q24 — Area and Volume · easy · theory
A parallelogram has sides $3$ and $4$ units at right angles. Its area is
A. $6$ sq units
B. $12$ sq units ✓ Correct
C. $7$ sq units
D. $24$ sq units
Solution: Area $= ab\sin 90^\circ = 3\times4 = 12$ sq units (a rectangle).
Q25 — Area and Volume · easy · theory
Two sides of a triangle are equal vectors of magnitude $a$ with angle $\theta$ between them. The area of the triangle is
A. $a^2(1-\cos\theta)$
B. $a^2\sin\theta$
C. $\frac{1}{2}a^2\cos\theta$
D. $\frac{1}{2}a^2\sin\theta$ ✓ Correct
Solution: Area $= \tfrac{1}{2}|\vec A\times\vec B| = \tfrac{1}{2}a\cdot a\sin\theta$.
Q26 — Area and Volume · easy · theory
For fixed side lengths, the area of a parallelogram is maximum when the angle between the sides is
A. $45^\circ$
B. $180^\circ$
C. $90^\circ$ ✓ Correct
D. $60^\circ$
Solution: Area $= ab\sin\theta$ peaks at $\sin\theta = 1$, i.e. $\theta = 90^\circ$.
Q27 — Area and Volume · easy · theory
If $\vec A \times \vec B = 3\hat{k}$, the area of the triangle formed with $\vec A$ and $\vec B$ as adjacent sides is
A. $3$ sq units
B. $\sqrt{3}$ sq units
C. $6$ sq units
D. $\frac{3}{2}$ sq units ✓ Correct
Solution: Triangle area $= \tfrac{1}{2}|\vec A\times\vec B| = \tfrac{3}{2}$ sq units.
Q28 — Area and Volume · easy · theory
A rhombus has diagonals of lengths $6$ and $8$ units. Its area is
A. $14$ sq units
B. $12$ sq units
C. $48$ sq units
D. $24$ sq units ✓ Correct
Solution: Area $= \tfrac{1}{2}d_1 d_2 = \tfrac{1}{2}(6)(8) = 24$ sq units.
Q29 — Area and Volume · easy · theory
A parallelogram has sides $6$ and $8$ units. Its maximum possible area is
A. $48$ sq units ✓ Correct
B. $96$ sq units
C. $14$ sq units
D. $24$ sq units
Solution: Maximum at $\theta = 90^\circ$: area $= 6\times8 = 48$ sq units.
Q30 — Area and Volume · easy · theory
The direction of the area vector of a plane surface is
A. Along a diagonal
B. Along the longest side
C. Perpendicular to the surface ✓ Correct
D. Parallel to the surface
Solution: By convention (right-hand rule), an area vector points along the normal to the surface.