A\cos\theta and A\sin\theta. The angle is measured from the x-axis, so the horizontal component carries the cosine.

\tan\theta = \dfrac{A_y}{A_x}. The angle is measured from the positive x-axis.

10. A_x = 20\cos 60^\circ = 20 \times 0.5 = 10.

Question 1

Resolution of a vector means:

Accepted Answer

Splitting it into components along chosen directions. It is the reverse process of vector addition.

Question 2

The rectangular components of a vector \vec{A} making an angle 	heta with the x-axis are:

Accepted Answer

A\cos	heta and A\sin	heta. The angle is measured from the x-axis, so the horizontal component carries the cosine.

Question 3

The magnitude of a vector in terms of its rectangular components is:

Accepted Answer

\sqrt{A_x^2 + A_y^2}. The components form the perpendicular sides of a right triangle whose hypotenuse is the vector.

Question 4

The direction of a vector in terms of its components is given by:

Accepted Answer

an	heta = \dfrac{A_y}{A_x}. The angle is measured from the positive x-axis.

Question 5

In three dimensions, a vector can be resolved into:

Accepted Answer

Three mutually perpendicular components. These are written A_x\hat{i} + A_y\hat{j} + A_z\hat{k}.

Question 6

The direction cosines of a vector are the cosines of the angles it makes with the:

Accepted Answer

Three coordinate axes. They satisfy \cos^2\alpha + \cos^2\beta + \cos^2\gamma = 1.

Question 7

A vector can be resolved into components along:

Accepted Answer

Any two non-parallel directions in its plane. Rectangular resolution is merely the most convenient special case.

Question 8

When a vector is resolved into two perpendicular components, the sum of the magnitudes of the components is:

Accepted Answer

Generally greater than the magnitude of the vector. Components add as vectors, not as numbers: 3 + 4 = 7 while the vector has magnitude 5.

Question 9

A vector of magnitude 10 makes 30^\circ with the x-axis. Its x and y components are approximately:

Accepted Answer

8.66 and 5. A_x = 10\cos 30^\circ \approx 8.66 and A_y = 10\sin 30^\circ = 5.

Question 10

A vector of magnitude 20 makes 60^\circ with the x-axis. Its x component is:

Accepted Answer

10. A_x = 20\cos 60^\circ = 20 	imes 0.5 = 10.

Question 11

A vector of magnitude 100 makes 45^\circ with the x-axis. Each of its components is approximately:

Accepted Answer

70.7. 100\cos 45^\circ = 100\sin 45^\circ \approx 70.7.

Question 12

A vector has components 3 and 4 along the x and y axes. Its magnitude and direction are:

Accepted Answer

5 at 	an^{-1}\left(\dfrac{4}{3}ight) to the x-axis. A = \sqrt{9 + 16} = 5 and 	an	heta = \dfrac{A_y}{A_x} = \dfrac{4}{3}, giving about 53.1^\circ.

Question 13

A force of 50	ext{ N} acts at 37^\circ to the horizontal. Its horizontal component is approximately (\cos 37^\circ = 0.8):

Accepted Answer

40	ext{ N}. F_x = 50 	imes 0.8 = 40	ext{ N}.

Question 14

For the same force of 50	ext{ N} at 37^\circ, the vertical component is approximately (\sin 37^\circ = 0.6):

Accepted Answer

30	ext{ N}. F_y = 50 	imes 0.6 = 30	ext{ N}.

Question 15

A projectile is launched at 20	ext{ m/s} at 30^\circ to the horizontal. Its horizontal component of velocity is approximately:

Accepted Answer

17.3	ext{ m/s}. v_x = 20\cos 30^\circ \approx 17.3	ext{ m/s}.

Question 16

For the same projectile (20	ext{ m/s} at 30^\circ), the vertical component of velocity is:

Accepted Answer

10	ext{ m/s}. v_y = 20\sin 30^\circ = 10	ext{ m/s}.

Question 17

A vector of magnitude 13 has an x component of 5. Its y component is:

Accepted Answer

12. A_y = \sqrt{13^2 - 5^2} = \sqrt{144} = 12.

Question 18

A block of weight 100	ext{ N} rests on an incline of 30^\circ. The component of its weight along the incline is:

Accepted Answer

50	ext{ N}. The component along the surface is W\sin	heta = 100 	imes 0.5 = 50	ext{ N}.

Question 19

For the same block on the 30^\circ incline, the component of weight perpendicular to the surface is approximately:

Accepted Answer

86.6	ext{ N}. The perpendicular component is W\cos	heta = 100 	imes 0.866 \approx 86.6	ext{ N}.

Question 20

A vector has equal x and y components. The angle it makes with the x-axis is:

Accepted Answer

45^\circ. 	an	heta = \dfrac{A_y}{A_x} = 1, so 	heta = 45^\circ.

Resolution of Vectors & Components — MH-CET Physics MCQs with Solutions

Questions with solutions