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Physics · MOTION IN A PLANE
हिन्दीTwo vectors \( \mathbf{A} \) and \( \mathbf{B} \) of equal magnitude \( A \) are inclined at an angle \( \theta \). If the magnitude of their vector sum \( |\mathbf{A} + \mathbf{B}| \) is \( \sqrt{3} \) times the magnitude of their vector difference \( |\mathbf{A} - \mathbf{B}| \), determine the angle \( \theta \).
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Correct answer · Option A
\( 60^\circ \)
Explanation
\( |\mathbf{A} + \mathbf{B}| = 2A \cos(\theta/2) \) and \( |\mathbf{A} - \mathbf{B}| = 2A \sin(\theta/2) \). Given \( 2A\cos(\theta/2) = \sqrt{3} \times 2A\sin(\theta/2) \implies \cot(\theta/2) = \sqrt{3} \implies \theta/2 = 30^\circ \implies \theta = 60^\circ \).
