Q: 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

5\sqrt{5}, \tan^{-1}(1/2). \vec{A} - \vec{B} = -2\hat{i} - 5\hat{j}. Magnitude = \sqrt{4 + 25} = \sqrt{29}. Direction = \tan^{-1}(5/2).

Q: 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

2mv\sin\theta. Change in momentum = 2mv\sin\theta (perpendicular component changes sign).

Question 1

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?

Accepted Answer

0°, 180° and 90°. For resultant = 17 N (max), angle = 0°. For resultant = 7 N (min), angle = 180°. For resultant = 13 N, angle = 90°.

Question 2

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

Accepted Answer

5\sqrt{5}, 	an^{-1}(1/2). \vec{A} - \vec{B} = -2\hat{i} - 5\hat{j}. Magnitude = \sqrt{4 + 25} = \sqrt{29}. Direction = 	an^{-1}(5/2).

Question 3

A truck travelling due north at 20 m/s turns west and travels at the same speed. The change in its velocity is

Accepted Answer

20\sqrt{2} m/s N–W. Initial velocity = 20 m/s north, Final = 20 m/s west. Change = \sqrt{20^2 + 20^2} = 20\sqrt{2} in N-W direction.

Question 4

If the sum of two unit vectors is a unit vector, then magnitude of difference is

Accepted Answer

\sqrt{3}. For two unit vectors with sum as unit vector, angle between them is 120°. Difference magnitude = \sqrt{3}.

Question 5

If \vec{A} = 2\hat{i} - \hat{j}, \vec{B} = 3\hat{j} - \hat{k} and \vec{C} = 6\hat{i} - 2\hat{k}, Value of \vec{A} + 2\vec{B} - 3\vec{C} would be

Accepted Answer

-20\hat{i} + 5\hat{j} - 4\hat{k}. \vec{A} + 2\vec{B} - 3\vec{C} = 2\hat{i} - \hat{j} + 6\hat{j} - 2\hat{k} - 18\hat{i} + 6\hat{k} = -20\hat{i} + 5\hat{j} + 4\hat{k}.

Question 6

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

Accepted Answer

2mv\sin	heta. Change in momentum = 2mv\sin	heta (perpendicular component changes sign).

Question 7

Two forces, each of magnitude F have a resultant of the same magnitude F. The angle between the two forces is

Accepted Answer

120°. For equal forces with resultant equal to F: F^2 = F^2 + F^2 + 2F^2\cos	heta. This gives \cos	heta = -1/2, so 	heta = 120°.

Question 8

For the resultant of the two vectors to be maximum, what must be the angle between them

Accepted Answer

0°. Resultant is maximum when vectors are parallel (angle = 0°).

Question 9

A particle is simultaneously acted by two forces equal to 4 N and 3 N. The net force on the particle is

Accepted Answer

Between 1 N and 7 N. Resultant can vary from |4-3| = 1 N to 4+3 = 7 N depending on angle.

Question 10

A particle is simultaneously acted by two forces of 4 N and 3 N and then lies outside this plane. The resultant \vec{A} + \vec{B} + \vec{C}

Accepted Answer

Cannot be zero. If C lies outside the plane, the resultant cannot be zero.

Question 11

If the resultant of two forces be smaller than the magnitude of larger force, the two forces must be

Accepted Answer

Different both in magnitude and direction. Resultant less than larger force means they are not aligned and must be in different directions.

Question 12

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

Accepted Answer

\sqrt{F_1^2 + F_2^2}. For perpendicular forces, resultant = \sqrt{F_1^2 + F_2^2} (Pythagorean theorem).

Question 13

If |\vec{A} + \vec{B}| = |\vec{A}| + |\vec{B}|, the angle between \vec{A} and \vec{B} is

Accepted Answer

0°. This equality holds only when vectors are parallel (0° angle).

Question 14

Let the angle between two nonzero vectors \vec{A} and \vec{B} be 120° and resultant be \vec{C}

Accepted Answer

C must be greater than |A-B|. For 120° angle, the resultant can be greater than the difference.

Question 15

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

Accepted Answer

90°. Since 12^2 + 5^2 = 13^2 (144 + 25 = 169), vectors are perpendicular.

Question 16

Magnitude of vector which comes on addition of two vectors, 6\hat{i} + 7\hat{j} and 3\hat{i} + 4\hat{j} is

Accepted Answer

\sqrt{202}. Sum = 9\hat{i} + 11\hat{j}. Magnitude = \sqrt{81 + 121} = \sqrt{202}.

Question 17

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

Accepted Answer

14.31 m. Total displacement = \sqrt{12^2 + 5^2 + 6^2} = \sqrt{144 + 25 + 36} = \sqrt{205} \approx 14.31 m.

Question 18

The three vectors \vec{A} = 3\hat{i} + 2\hat{j} + \hat{k}, \vec{B} = \hat{i} + 3\hat{j} + 5\hat{k} and \vec{C} = 2\hat{i} + \hat{j} + 4\hat{k} form

Accepted Answer

A right angled triangle. |A|^2 = 14, |B|^2 = 35, |C|^2 = 21. Since 14 + 21 = 35, it forms a right triangle.

Question 19

For the figure shown, \vec{A} + \vec{B} equals

Accepted Answer

\vec{C}. From the vector diagram, \vec{A} + \vec{B} = \vec{C}.

Question 20

Let \vec{C} = \vec{A} + \vec{B}, then

Accepted Answer

It is possible to have |C| < |A| and |C| < |B|. When vectors are opposite, |C| can be less than both |A| and |B|.

Addition and Subtraction — NEET Physics MCQs with Solutions

Questions with solutions