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
|→P−→Q|
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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+Q2−2.PQ .P2Q |→R|=|→Q|, hence option (c) is correct.