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Physics · MOTION IN A PLANE
हिन्दीTwo vectors \( \mathbf{A} \) and \( \mathbf{B} \) have equal magnitudes \( F \). If the magnitude of their resultant vector \( \mathbf{R} = \mathbf{A} + \mathbf{B} \) is also equal to \( F \), what is the angle between \( \mathbf{A} \) and \( \mathbf{B} \), and what is the magnitude of their vector difference \( |\mathbf{A} - \mathbf{B}| \)?
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Correct answer · Option B
\( 120^\circ \) and \( \sqrt{3}F \)
Explanation
Using \( R^2 = A^2 + B^2 + 2AB\cos\theta \implies F^2 = 2F^2(1 + \cos\theta) \implies \cos\theta = -1/2 \implies \theta = 120^\circ \). The magnitude of vector difference is \( |\mathbf{A} - \mathbf{B}| = \sqrt{F^2 + F^2 - 2F^2\cos 120^\circ} = \sqrt{3}F \).
