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Question

The resultant of two vectors P and Q is R. If magnitude of Q is doubled, the new resultant is perpendicular to P. Then |R| equals

A
|P|
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B
|(P+Q)|
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C
|Q|
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D
|PQ|
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Solution

The correct option is C |Q|
When Q is doubled, angle between new resultant and P, can be written as
tan α=2Q sin θP+2Q cos θ
Given that α=90
P+2Q cos θ=0
cos θ=P2Q
|R|=P2+Q2+2PQ cos θ
=P2+Q22.PQ .P2Q
|R|=|Q|, hence option (c) is correct.

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