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Q.

If the angle between two vectors of equal magnitude P is $θ then$ the magnitude of the resultant vector is

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a

$2 P \cos θ$

b

$2 P \cos \frac{θ}{2}$

c

$2 P \sin θ$

d

$2 P \sin \frac{θ}{2}$

answer is A.

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Detailed Solution

$|\vec{P}| = |\vec{Q}| = P$

$R = \sqrt{P^{2} + P^{2} + 2 P^{2} \cos θ}$

$= \sqrt{2 P^{2} (1 + \cos θ)}$

$= \sqrt{2 P^{2} .2 \cos^{2} (θ /2)}$

$= 2 Pcos (θ /2)$

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