Question

For two vectors $ \mathbf{A} $ and $ \mathbf{B} $, if $ \mathbf{A} + \mathbf{B} = |\mathbf{A} - \mathbf{B}| $, then

• A. \( \mathbf{A} \) and \( \mathbf{B} \) are parallel vectors.
• B. \( \mathbf{A} \) and \( \mathbf{B} \) are opposite vectors.
• C. \( \mathbf{A} \) and \( \mathbf{B} \) are perpendicular to each other.
• D. Angle between \( \mathbf{A} \) and \( \mathbf{B} \) is \( 120^\circ \).

Hint:

In vector questions involving equality of magnitudes, check the condition of perpendicularity first when the equation involves the difference of the vectors.

Answer 1

The Correct Option is C

The equation \( \mathbf{A} + \mathbf{B} = |\mathbf{A} - \mathbf{B}| \) implies that the vectors \( \mathbf{A} \) and \( \mathbf{B} \) are perpendicular. This can be shown by applying the Pythagorean theorem to the vector magnitudes and realizing that the sum of squares of the magnitudes of the vectors on both sides must be equal. This condition is satisfied only when the vectors are perpendicular.