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Physics · MOTION IN A PLANE
हिन्दीMatch List-I with List-II: List-I List-II A Magnitude of resultant vector \( R \) I \( \sqrt{A^2+B^2+2AB\cos\theta} \) B Direction angle \( \tan\alpha \) of resultant II \( \frac{B\sin\theta}{A+B\cos\theta} \) C Law of sines for vector triangle III \( \frac{R}{\sin\theta} = \frac{A}{\sin\beta} = \frac{B}{\sin\alpha} \) D Condition for maximum resultant magnitude IV \( \theta = 0^\circ \) Choose the correct answer from the options given below:
Match List-I with List-II:
| List-I | List-II | ||
|---|---|---|---|
| A | Magnitude of resultant vector \( R \) | I | \( \sqrt{A^2+B^2+2AB\cos\theta} \) |
| B | Direction angle \( \tan\alpha \) of resultant | II | \( \frac{B\sin\theta}{A+B\cos\theta} \) |
| C | Law of sines for vector triangle | III | \( \frac{R}{\sin\theta} = \frac{A}{\sin\beta} = \frac{B}{\sin\alpha} \) |
| D | Condition for maximum resultant magnitude | IV | \( \theta = 0^\circ \) |
Choose the correct answer from the options given below:
Correct answer · Option B
A-(I), B-(II), C-(III), D-(IV)
Explanation
From vector addition theory, \( R = \sqrt{A^2+B^2+2AB\cos\theta} \), \( \tan\alpha = \frac{B\sin\theta}{A+B\cos\theta} \), law of sines is \( \frac{R}{\sin\theta} = \frac{A}{\sin\beta} = \frac{B}{\sin\alpha} \), and maximum magnitude occurs when \( \theta = 0^\circ \).
