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Question: The resultant of two vectors \(\overset{\rightarrow}{P}\) and \(\overset{\rightarrow}{Q}\)is \(\over...

The resultant of two vectors P→\overset{\rightarrow}{P} and Q→\overset{\rightarrow}{Q}is R→\overset{\rightarrow}{R}. If the magnitude of Q→\overset{\rightarrow}{Q} is doubled, the new resultant becomes perpendicular toP→\overset{\rightarrow}{P}, then the magnitude of R→\overset{\rightarrow}{R}is –

A

P2−Q2PQ\frac{P^{2} - Q}{2PQ}

B

P+QP−Q\frac{P + Q}{P - Q}

C

Q

D

PQ\frac{P}{Q}

Answer

Q

Explanation

Solution

R = P2+2PQcos⁡θ+Q2\sqrt{P^{2} + 2PQ\cos\theta + Q^{2}} …(1)

tan 900 = 2Qsin⁡θP+2Qcos⁡θ\frac{2Q\sin\theta}{P + 2Q\cos\theta} = 10\frac{1}{0}

P + 2Q cos q = 0

from (1)R = P(P+2Qcos⁡θ)+Q2\sqrt{P(P + 2Q\cos\theta) + Q^{2}}

R = Q