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Question

Magnitude of resultant of two vectors P and Q is equal to the magnitude of P. Find the angle between Q and the resultant of 2P and Q.

A
90.
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B
60.
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C
75.
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D
90.
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Solution

The correct option is D 90.
Given P+Q=P
Let θ be the angle between P and Q.
P2+Q2+2PQcosθ=P2
Q+2Pcosθ=0
cosθ=Q2P


tanα=2Psinθ2Pcosθ+Q=
[2Pcosθ+Q=0]
or α=90

Alternate solution:
From the figure below, making use of the fact that |P|=|P+Q|


Angle between (2P+Q) and Q is 90.

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