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Physics · MOTION IN A PLANE
हिन्दीTwo vectors \( \mathbf{A} \) and \( \mathbf{B} \) have equal magnitudes \( A \) and are separated by an angle \( \theta \). If their resultant vector \( \mathbf{R} \) makes an angle \( \alpha \) with vector \( \mathbf{A} \), determine the relation between \( \alpha \) and \( \theta \), and the expression for the magnitude of \( \mathbf{R} \).
Correct answer · Option 4
\( \alpha = \theta/2 \), \( R = 2A \cos(\theta/2) \)
Explanation
For equal magnitude vectors, the resultant bisects the angle, so \( \alpha = \theta/2 \). Magnitude \( R = \sqrt{A^2 + A^2 + 2A^2\cos\theta} = \sqrt{2A^2(1+\cos\theta)} = 2A\cos(\theta/2) \).
