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Addition and Subtraction — JEE Main Physics MCQs with Solutions

Free JEE Main Physics Addition and Subtraction MCQs with step-by-step solutions (71 questions). Part of Vectors. Practise online on Prepizo — no login needed.

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Questions with solutions

Q1 — Addition and Subtraction · easy
There are two force vectors, one of 5 N and other of 12 N. If the resultant of the two forces has a magnitude of 17 N, 7 N and 13 N respectively, at what angle the two vectors be added to get these resultants?
A. 0°, 180° and 90°  ✓ Correct
B. 0°, 90° and 180°
C. 0°, 90° and 90°
D. 180°, 0° and 90°
Solution: For resultant = 17 N (max), angle = 0°. For resultant = 7 N (min), angle = 180°. For resultant = 13 N, angle = 90°.
Q2 — Addition and Subtraction · easy
For the resultant of the two vectors to be maximum, what must be the angle between them
A. 0°  ✓ Correct
B. 60°
C. 90°
D. 180°
Solution: Resultant is maximum when vectors are parallel (angle = 0°).
Q3 — Addition and Subtraction · easy
A particle is simultaneously acted by two forces equal to 4 N and 3 N. The net force on the particle is
A. 7 N
B. 5 N
C. 1 N
D. Between 1 N and 7 N  ✓ Correct
Solution: Resultant can vary from |4-3| = 1 N to 4+3 = 7 N depending on angle.
Q4 — Addition and Subtraction · easy
Forces $\vec{F}_1$ and $\vec{F}_2$ act on a point mass in two mutually perpendicular directions. The resultant force on the point mass will be
A. $F_1 + F_2$
B. $F_1 - F_2$
C. $\sqrt{F_1^2 + F_2^2}$  ✓ Correct
D. $\sqrt{F_1^2 - F_2^2}$
Solution: For perpendicular forces, resultant = $\sqrt{F_1^2 + F_2^2}$ (Pythagorean theorem).
Q5 — Addition and Subtraction · easy
If $|\vec{A} + \vec{B}| = |\vec{A}| + |\vec{B}|$, the angle between $\vec{A}$ and $\vec{B}$ is
A. 60°
B. 0°  ✓ Correct
C. 120°
D. 90°
Solution: This equality holds only when vectors are parallel (0° angle).
Q6 — Addition and Subtraction · easy
The magnitude of vectors $\vec{A}$, $\vec{B}$ and $\vec{C}$ are respectively 12, 5 and 13 units and $\vec{A} + \vec{B} = \vec{C}$, then the angle between $\vec{A}$ and $\vec{B}$ is
A. 90°  ✓ Correct
B. 60°
C. 120°
D. 45°
Solution: Since $12^2 + 5^2 = 13^2$ (144 + 25 = 169), vectors are perpendicular.
Q7 — Addition and Subtraction · easy
Magnitude of vector which comes on addition of two vectors, $6\hat{i} + 7\hat{j}$ and $3\hat{i} + 4\hat{j}$ is
A. $\sqrt{136}$
B. $13.2$
C. $\sqrt{202}$  ✓ Correct
D. $\sqrt{160}$
Solution: Sum = $9\hat{i} + 11\hat{j}$. Magnitude = $\sqrt{81 + 121} = \sqrt{202}$.
Q8 — Addition and Subtraction · easy
A particle has displacement of 12 m towards east and 5 m towards north then 6 m vertically upward. The sum of these displacements is
A. 12 m
B. 10.04 m
C. 14.31 m  ✓ Correct
D. None of these
Solution: Total displacement = $\sqrt{12^2 + 5^2 + 6^2} = \sqrt{144 + 25 + 36} = \sqrt{205} \approx 14.31$ m.
Q9 — Addition and Subtraction · easy
For the figure shown, $\vec{A} + \vec{B}$ equals
A. $\vec{C}$  ✓ Correct
B. $\vec{B} + \vec{C}$
C. $\vec{C} + \vec{A}$
D. $\vec{A} + \vec{B} + \vec{C} = 0$
Solution: From the vector diagram, $\vec{A} + \vec{B} = \vec{C}$.
Q10 — Addition and Subtraction · easy
The value of the sum of two vectors $\vec{A}$ and $\vec{B}$ with θ as the angle between them is
A. $\sqrt{A^2 + B^2 + 2AB\cos\theta}$  ✓ Correct
B. $\sqrt{A^2 + B^2 - 2AB\cos\theta}$
C. $\sqrt{A^2 + B^2 + 2AB\sin\theta}$
D. $\sqrt{A^2 + B^2 - 2AB\sin\theta}$
Solution: This is the law of cosines for vector addition.
Q11 — Addition and Subtraction · easy
A body is at rest under the action of three forces, two of which are $\vec{F}_1 = 4\hat{i}$, $\vec{F}_2 = 6\hat{j}$, the third force is
A. $4\hat{i} + 6\hat{j}$
B. $-4\hat{i} + 6\hat{j}$
C. $-4\hat{i} - 6\hat{j}$  ✓ Correct
D. $4\hat{i} - 6\hat{j}$
Solution: For equilibrium: $\vec{F}_3 = -(\vec{F}_1 + \vec{F}_2) = -4\hat{i} - 6\hat{j}$.
Q12 — Addition and Subtraction · easy
What displacement must be added to the displacement $25\hat{i} + 6\hat{j}$ m to give a displacement of 7.0 m pointing in the x- direction
A. $-18\hat{i} - 6\hat{j}$  ✓ Correct
B. $32\hat{i} - 13\hat{j}$
C. $18\hat{i} + 6\hat{j}$
D. $25\hat{i} - 13\hat{j}$
Solution: Required displacement = $7\hat{i} - (25\hat{i} + 6\hat{j}) = -18\hat{i} - 6\hat{j}$.
Q13 — Addition and Subtraction · easy
A body moves due East with velocity 20 km/hour and then due North with velocity 15 km/hour. The resultant velocity
A. 5 km/hour
B. 15 km/hour
C. 20 km/hour
D. 25 km/hour  ✓ Correct
Solution: Resultant = $\sqrt{20^2 + 15^2} = \sqrt{400 + 225} = \sqrt{625} = 25$ km/hr.
Q14 — Addition and Subtraction · easy
The magnitudes of vectors $\vec{A}$, $\vec{B}$ and $\vec{C}$ are 3, 4 and 5 units respectively. If $\vec{A} + \vec{B} = \vec{C}$, the angle between $\vec{A}$ and $\vec{B}$ is
A. $\pi/2$  ✓ Correct
B. $\cos^{-1}(0.6)$
C. $\tan^{-1}(7/5)$
D. $3\pi/4$
Solution: Since $3^2 + 4^2 = 5^2$, angle = π/2.
Q15 — Addition and Subtraction · easy
A person goes 10 km north and 20 km east. What will be displacement from initial point
A. 22.36 km  ✓ Correct
B. 2 km
C. 5 km
D. 20 km
Solution: Displacement = $\sqrt{10^2 + 20^2} = \sqrt{500} \approx 22.36$ km.
Q16 — Addition and Subtraction · easy
If $|\vec{A} + \vec{B}| = |\vec{A}| + |\vec{B}|$, then angle between $\vec{A}$ and $\vec{B}$ will be
A. 90°
B. 120°
C. 0°  ✓ Correct
D. 60°
Solution: This equality holds only when vectors are parallel (0° angle).
Q17 — Addition and Subtraction · easy
y component of velocity is 20 and x component of velocity is 10. The direction of motion of the body with the horizontal at this instant is
A. $\tan^{-1}(2)$  ✓ Correct
B. $\tan^{-1}(1/2)$
C. 45°
D. 0°
Solution: Direction = $\tan^{-1}(v_y/v_x) = \tan^{-1}(20/10) = \tan^{-1}(2)$.
Q18 — Addition and Subtraction · easy
Two forces of 12 N and 8 N act upon a body. The resultant force on the body has maximum value of
A. 4 N
B. 0 N
C. 20 N  ✓ Correct
D. 8 N
Solution: Maximum resultant = 12 + 8 = 20 N (when forces are parallel).
Q19 — Addition and Subtraction · easy
The vectors $5\hat{i} + 8\hat{j}$ and $2\hat{i} + 7\hat{j}$ are added. The magnitude of the sum of these vectors is
A. $\sqrt{274}$  ✓ Correct
B. 38
C. $\sqrt{238}$
D. $\sqrt{560}$
Solution: Sum = $7\hat{i} + 15\hat{j}$. Magnitude = $\sqrt{49 + 225} = \sqrt{274}$.
Q20 — Addition and Subtraction · easy
A particle starting from the origin (0,0) moves in a straight line in the (x,y) plane, its coordinates at a later time are $(\sqrt{3}, 3)$. The path the particle makes with x-axis, is inclined at an angle of:
A. 45°
B. 60°  ✓ Correct
C. 30°
D. 90°
Solution: Angle = $\tan^{-1}(3/\sqrt{3}) = \tan^{-1}(\sqrt{3})$ = 60°.
Q21 — Addition and Subtraction · easy
Two equal forces act at a point and are inclined to each other at an angle of 60°. The magnitude of their resultant is:
A. $\sqrt{3}A$  ✓ Correct
B. $2A$
C. $3A$
D. $\sqrt{2}A$
Solution: Resultant = $\sqrt{A^2 + A^2 + 2A^2\cos(60°)} = \sqrt{3A^2} = \sqrt{3}A$.
Q22 — Addition and Subtraction · easy
If vectors $\hat{i} - 3\hat{j} + 5\hat{k}$ and $\hat{i} - 3\hat{j} - a\hat{k}$ are equal vectors then the value of a is:
A. 5
B. 4
C. -4
D. -5  ✓ Correct
Solution: For equal vectors, all components must be equal. $5 = -a$, so $a = -5$.
Q23 — Addition and Subtraction · easy
If the magnitudes of vectors $\vec{A}$, $\vec{B}$ and $\vec{C}$ are 4, 3 and 5 units respectively and $\vec{A} + \vec{B} = \vec{C}$, the angle between vectors $\vec{A}$ and $\vec{B}$ is:
A. 90°  ✓ Correct
B. $\cos^{-1}(0.6)$
C. 30°
D. $\tan^{-1}(12/5)$
Solution: Since $4^2 + 3^2 = 5^2$, angle = 90°.
Q24 — Addition and Subtraction · easy
Two vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$ then the angle between the two vectors $\vec{A}$ and $\vec{B}$ will be:
A. 0°
B. $\frac{\pi}{3}$
C. $\frac{\pi}{4}$
D. $\frac{\pi}{2}$  ✓ Correct
Solution: This condition means vectors are perpendicular. Angle = π/2.
Q25 — Addition and Subtraction · easy
If angle between $\vec{A}$ and $\vec{B}$ is 30°, then find the angle between $3\vec{A}$ and $-2\vec{B}$
A. 30°
B. 150°  ✓ Correct
C. 180°
D. 90°
Solution: Angle between $3\vec{A}$ and $-2\vec{B}$ = 180° - 30° = 150°.
Q26 — Addition and Subtraction · hard
An object of m kg with speed of v m/s strikes a wall at an angle θ and rebounds at the same speed and same angle. The magnitude of the change in momentum of the object will be
A. 0
B. mv
C. mv/2
D. $2mv\sin\theta$  ✓ Correct
Solution: Change in momentum = $2mv\sin\theta$ (perpendicular component changes sign).
Q27 — Addition and Subtraction · hard
Let the angle between two nonzero vectors $\vec{A}$ and $\vec{B}$ be 120° and resultant be $\vec{C}$
A. $C$ must be equal to $|A-B|$
B. $C$ must be less than $|A-B|$
C. $C$ must be greater than $|A-B|$  ✓ Correct
D. $C$ may be equal to $|A-B|$
Solution: For 120° angle, the resultant can be greater than the difference.
Q28 — Addition and Subtraction · hard
The sum of two forces acting at a point is 16 N. If the resultant force is 8 N and its direction is perpendicular to minimum force then the forces are
A. 6 N and 10 N  ✓ Correct
B. 8 N and 8 N
C. 4 N and 12 N
D. 2 N and 14 N
Solution: Let forces be A and B. A + B = 16 and resultant R = 8. Using vector diagram analysis: A = 6 N, B = 10 N.
Q29 — Addition and Subtraction · hard
The resultant of two vectors $\vec{A}$ and $\vec{B}$ is perpendicular to the vector $\vec{A}$ and its magnitude is equal to half the magnitude of vector $\vec{B}$. The angle between $\vec{A}$ and $\vec{B}$ is
A. 120°
B. 150°  ✓ Correct
C. 135°
D. None of these
Solution: Using perpendicularity condition and magnitude relation: angle = 150°.
Q30 — Addition and Subtraction · hard
The resultant of $\vec{P}$ and $\vec{Q}$ is perpendicular to $\vec{P}$. What is the angle between $\vec{P}$ and $\vec{Q}$
A. $\cos^{-1}(P/Q)$
B. $\cos^{-1}(-P/Q)$  ✓ Correct
C. $\sin^{-1}(P/Q)$
D. $\sin^{-1}(-P/Q)$
Solution: For perpendicular resultant: $\cos\theta = -P/Q$.