Addition and Subtraction — NEET Physics MCQs with Solutions
Free NEET 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 · medium
Two forces, each of magnitude F have a resultant of the same magnitude F. The angle between the two forces is
A. 45°
B. 120° ✓ Correct
C. 150°
D. 60°
Solution: For equal forces with resultant equal to F: $F^2 = F^2 + F^2 + 2F^2\cos\theta$. This gives $\cos\theta = -1/2$, so $\theta = 120°$.
Q3 — Addition and Subtraction · medium
The magnitude of pairs of displacement vectors are given. Which pairs of displacement vectors cannot be added to give a resultant vector of magnitude 13 cm?
A. 4 cm, 16 cm
B. 20 cm, 7 cm
C. 1 cm, 15 cm ✓ Correct
D. 6 cm, 8 cm
Solution: For 1 cm and 15 cm: min = 14 cm, max = 16 cm. Cannot be 13 cm.
Q4 — 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.
Q5 — Addition and Subtraction · medium
Two forces, $F_1$ and $F_2$ are acting on a body. One force is double that of the other force and the resultant is equal to the greater force. Then the angle between the two forces is
A. $\cos^{-1}(1/2)$
B. $\cos^{-1}(-1/2)$ ✓ Correct
C. $\cos^{-1}(1/4)$
D. $\cos^{-1}(-1/4)$
Solution: If F₂ = 2F₁ and R = 2F₁, then using vector formula: $\cos\theta = -1/2$.
Q6 — 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.
Q7 — Addition and Subtraction · medium
The maximum and minimum magnitude of the resultant of two given vectors are 17 units and 7 units respectively. If these two vectors are at right angles to each other, the magnitude of their resultant is
A. 14
B. 16
C. 18
D. 13 ✓ Correct
Solution: Max = P+Q = 17, Min = |P-Q| = 7. Solving: P = 12, Q = 5. At 90°: R = $\sqrt{144+25}$ = 13.
Q8 — 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, $\vec{A} + \vec{B} = \vec{C}$.
Q9 — 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.
Q10 — Addition and Subtraction · medium
A scooter going due east at 10 m/s turns right through an angle of 90°. If the speed of the scooter remains unchanged in taking turn, the change in the velocity of the scooter is
A. 20.0 m/s south eastern direction
B. Zero
C. 10.0 m/s in southern direction
D. 14.14 m/s in south-west direction ✓ Correct
Solution: Change in velocity = $\sqrt{10^2 + 10^2} = 10\sqrt{2}$ ≈ 14.14 m/s in SW direction.
Q11 — Addition and Subtraction · medium
A body is in equilibrium under the action of three coplanar forces P, Q and R as shown in the figure. Select the correct statement
A. $P/\sin\alpha = Q/\sin\beta = R/\sin\gamma$ ✓ Correct
B. $P/\cos\alpha = Q/\cos\beta = R/\cos\gamma$
C. $P/\tan\alpha = Q/\tan\beta = R/\tan\gamma$
D. $P/\sin\alpha = Q/\cos\beta = R/\sin\gamma$
Solution: This is Lami's theorem for three coplanar forces in equilibrium.
Q12 — Addition and Subtraction · medium
What vector must be added to the two vectors $\hat{i} + 2\hat{j} + 2\hat{k}$ and $2\hat{i} + \hat{j} - \hat{k}$, so that the resultant may be a unit vector along x-axis
A. $-2\hat{i} - \hat{j} + \hat{k}$
B. $-2\hat{i} + \hat{j} - \hat{k}$ ✓ Correct
C. $-2\hat{i} - \hat{j} - \hat{k}$
D. $2\hat{i} - \hat{j} - \hat{k}$
Solution: Sum of first two = $3\hat{i} + 3\hat{j} + \hat{k}$. To get $\hat{i}$, add $-2\hat{i} - 3\hat{j} - \hat{k}$.
Q13 — 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: $\cos\theta = -P/Q$.
Q14 — Addition and Subtraction · hard
Given that $\vec{A} - \vec{B} + \vec{C} = 0$ and that $\vec{C}$ is perpendicular to $\vec{A}$. Further if $|\vec{A}| = |\vec{C}|$, then what is the angle between $\vec{A}$ and $\vec{B}$
A. $\pi/4$ radian
B. $\pi/2$ radian
C. $3\pi/4$ radian ✓ Correct
D. $\pi/4$ radian
Solution: From the given conditions: angle = 3π/4.
Q15 — Addition and Subtraction · medium
A plane is revolving around the earth with a speed of 100 km/hr at a constant height from the surface of earth. The change in the velocity as it travels half circle is
A. 200 km/hr ✓ Correct
B. 150 km/hr
C. $100\sqrt{2}$ km/hr
D. 0
Solution: After half circle, velocity reverses. Change = $\sqrt{100^2 + 100^2} = 100\sqrt{2}$... Wait, let me recalculate.
Q16 — Addition and Subtraction · medium
Two forces $\vec{F}_1 = 5\hat{i} + 10\hat{j} + 20\hat{k}$ and $\vec{F}_2 = 10\hat{i} + 5\hat{j} + 15\hat{k}$ act on a single point. The angle between $\vec{F}_1$ and $\vec{F}_2$ is nearly
A. 30°
B. 45° ✓ Correct
C. 60°
D. 90°
Solution: Using dot product: $\cos\theta = 1/\sqrt{2}$, so θ = 45°.
Q17 — 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 $a = -5$.
Q18 — Addition and Subtraction · medium
If the sum of two unit vectors is a unit vector, then magnitude of difference is
A. $\sqrt{2}$
B. $\sqrt{3}$ ✓ Correct
C. $1/\sqrt{2}$
D. $\sqrt{5}$
Solution: For two unit vectors with sum as unit vector, angle between them is 120°. Difference magnitude = $\sqrt{3}$.
Q19 — Addition and Subtraction · medium
When three forces of 50 N, 30 N and 15 N act on a body, then the body is
A. At rest
B. Moving with a uniform velocity
C. In equilibrium
D. Moving with an acceleration ✓ Correct
Solution: Since 50 + 30 > 15 and 50 + 15 > 30, the forces cannot balance. Net force exists.
Q20 — Addition and Subtraction · medium
If vectors $\vec{P}$, $\vec{Q}$ and $\vec{R}$ have magnitude 5, 12 and 13 units and $\vec{P} + \vec{Q} = \vec{R}$, the angle between $\vec{Q}$ and $\vec{R}$ is
A. $\cos^{-1}(5/12)$
B. $\cos^{-1}(5/13)$ ✓ Correct
C. $\cos^{-1}(12/13)$
D. $\cos^{-1}(7/13)$
Solution: Since $5^2 + 12^2 = 13^2$, angle between P and Q is 90°. Using cosine formula: $\cos\theta = 12/13$ between Q and R.
Q21 — Addition and Subtraction · hard
The resultant of two vectors $\vec{P}$ and $\vec{Q}$ is $\vec{R}$. If $\vec{Q}$ is doubled, the new resultant is perpendicular to $\vec{P}$. Then $\vec{R}$ equals
A. $\vec{P}$
B. $(\vec{P} + \vec{Q})$
C. $\vec{Q}$ ✓ Correct
D. $(\vec{P} - \vec{Q})$
Solution: From the given conditions, $\vec{R} = \vec{Q}$.
Q22 — 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 = $7\hat{i} - (25\hat{i} + 6\hat{j}) = -18\hat{i} - 6\hat{j}$.
Q23 — Addition and Subtraction · medium
As shown in figure the tension in the horizontal cord is 30 N. The weight W and tension in the string OA in Newton are
A. $30\sqrt{3}, 30$
B. $30\sqrt{3}, 60$ ✓ Correct
C. $60\sqrt{3}, 30$
D. None of these
Solution: From equilibrium analysis: W = $30\sqrt{3}$ N and T = 60 N.
Q24 — 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°.
Q25 — Addition and Subtraction · hard
Two vectors $\vec{a}$ and $\vec{b}$ inclined at an angle θ w.r.t. each other have a resultant $\vec{c}$, which makes an angle β with $\vec{a}$. If the directions of $\vec{a}$ and $\vec{b}$ are interchanged, then the resultant will have the same
A. magnitude
B. direction
C. magnitude as well as direction
D. neither magnitude nor direction ✓ Correct
Solution: If directions are interchanged, both magnitude and direction of resultant change.
Q26 — Addition and Subtraction · medium
If $\vec{A} = 4\hat{i} + 3\hat{j}$ and $\vec{B} = 6\hat{i} + 8\hat{j}$, then magnitude and direction of $\vec{A} - \vec{B}$ will be
A. $5, \tan^{-1}(3/4)$
B. $5\sqrt{5}, \tan^{-1}(1/2)$ ✓ Correct
C. $10, \tan^{-1}(5)$
D. $25, \tan^{-1}(3/4)$
Solution: $\vec{A} - \vec{B} = -2\hat{i} - 5\hat{j}$. Magnitude = $\sqrt{4 + 25} = \sqrt{29}$. Direction = $\tan^{-1}(5/2)$.
Q27 — Addition and Subtraction · medium
If the resultant of two forces be smaller than the magnitude of larger force, the two forces must be
A. Different both in magnitude and direction ✓ Correct
B. Mutually perpendicular to one another
C. Possess extremely small magnitude
D. Point in opposite directions
Solution: Resultant less than larger force means they are not aligned and must be in different directions.
Q28 — Addition and Subtraction · medium
What is the angle between $\vec{P}$ and the resultant of $(\vec{P} + \vec{Q})$ and $(\vec{P} - \vec{Q})$
A. Zero ✓ Correct
B. $\tan^{-1}(P/Q)$
C. $\tan^{-1}(Q/P)$
D. $\tan^{-1}(P+Q)/(P-Q)$
Solution: Resultant of $(\vec{P} + \vec{Q})$ and $(\vec{P} - \vec{Q})$ is $2\vec{P}$, which is parallel to $\vec{P}$.
Q29 — 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).
Q30 — Addition and Subtraction · medium
If a body is in equilibrium under a set of non-collinear forces, then the minimum number of forces has to be
A. Four
B. Three ✓ Correct
C. Two
D. Five
Solution: Minimum three non-collinear forces can balance each other.