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JEE · NEET Previous Year Question

$If two vectors A and B having equal magnitude R are inclined at angle θ, then$

Topic: JEE PYQ

Answer: A. Full step-by-step solution below.

A $| A + B | = 2 Rcos (\frac{θ}{2})$
B $| A - B | = 2 Rcos (\frac{θ}{2})$
C $| A - B | = 2 Rsin (\frac{θ}{2})$
D $| A + B | = 2 Rsin (\frac{θ}{2})$

Correct answer: A

Solution

(a) The magnitude of resultant vector R^{’} = a^{2} + b^{2} + 2 abcos θ Here a = b = R Then R^{’} = R^{2} + R^{2} + 2 R^{2} cos θ = R 2 1 + cos θ = 2 R 2 cos^{2} \frac{θ}{2} = 2 Rcos \frac{θ}{2}

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