Question 1

The triangle law of vector addition states that if two vectors are represented by two sides of a triangle taken in order, their resultant is represented by:

Accepted Answer

The third side taken in the reverse order. The closing side drawn from the tail of the first to the head of the second gives the resultant.

Question 2

The parallelogram law gives the resultant of two vectors as:

Accepted Answer

The diagonal of the parallelogram drawn from their common point. The magnitude is \sqrt{A^2 + B^2 + 2AB\cos	heta}.

Question 3

The polygon law of vector addition is used to find the resultant of:

Accepted Answer

More than two vectors. The vectors are drawn head to tail and the closing side gives the resultant.

Question 4

Vector addition is commutative, meaning that:

Accepted Answer

\vec{A} + \vec{B} = \vec{B} + \vec{A}. The order in which vectors are added does not affect the resultant.

Question 5

Vector addition is associative, meaning that:

Accepted Answer

(\vec{A} + \vec{B}) + \vec{C} = \vec{A} + (\vec{B} + \vec{C}). The grouping of three or more vectors does not affect their sum.

Question 6

The resultant of two vectors is maximum when the angle between them is:

Accepted Answer

0^\circ. With \cos 0^\circ = 1, the magnitudes simply add.

Question 7

The resultant of two vectors is minimum when the angle between them is:

Accepted Answer

180^\circ. Opposite vectors partly cancel, leaving the difference of the magnitudes.

Question 8

Subtraction of a vector \vec{B} from \vec{A} is carried out by:

Accepted Answer

Adding -\vec{B} to \vec{A}. Vector subtraction is simply addition of the reversed vector.

Question 9

If three forces acting on a body keep it in equilibrium, their resultant is:

Accepted Answer

A null vector. Equilibrium requires the vector sum of all forces to vanish.

Question 10

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

Accepted Answer

90^\circ. Squaring both sides gives 4\vec{A}\cdot\vec{B} = 0, so the vectors are perpendicular.

Question 11

Two vectors of magnitudes 3 and 4 act at 90^\circ. Their resultant is:

Accepted Answer

5. R = \sqrt{9 + 16} = 5.

Question 12

Two vectors of magnitudes 3 and 4 act in the same direction. Their resultant is:

Accepted Answer

7. With 	heta = 0^\circ the magnitudes add directly.

Question 13

Two vectors of magnitudes 3 and 4 act in opposite directions. Their resultant is:

Accepted Answer

1. With 	heta = 180^\circ the magnitudes subtract.

Question 14

Two equal vectors each of magnitude 5 act at 60^\circ. Their resultant is approximately:

Accepted Answer

8.66. R = \sqrt{25 + 25 + 2(25)(0.5)} = \sqrt{75} \approx 8.66.

Question 15

Two equal vectors each of magnitude 5 act at 120^\circ. Their resultant is:

Accepted Answer

5. R = \sqrt{25 + 25 - 25} = \sqrt{25} = 5.

Question 16

The maximum possible resultant of two vectors of magnitudes 6 and 8 is:

Accepted Answer

14. The maximum occurs when they are parallel: 6 + 8 = 14.

Question 17

The minimum possible resultant of two vectors of magnitudes 6 and 8 is:

Accepted Answer

2. The minimum occurs when they are antiparallel: |8 - 6| = 2.

Question 18

Two vectors of magnitudes 5 and 12 act at 90^\circ. Their resultant is:

Accepted Answer

13. R = \sqrt{25 + 144} = 13.

Question 19

Two equal vectors each of magnitude A act at 90^\circ. Their resultant is:

Accepted Answer

A\sqrt{2}. R = \sqrt{A^2 + A^2} = A\sqrt{2}.

Question 20

Two vectors each of magnitude 10 act in exactly opposite directions. Their resultant is:

Accepted Answer

Zero. Equal and opposite vectors cancel completely.

Addition & Subtraction of Vectors — MH-CET Physics MCQs with Solutions

Questions with solutions