A) \[\pi /3\]
B) \[\pi /4\]
C) \[\pi /5\]
D) \[\pi /6\]
Correct Answer: A
Solution :
Let angle between\[\overrightarrow{P}\]and\[\overrightarrow{Q}\]is\[\theta \]whose magnitude is R. Here,\[P=Q\]and \[{{R}^{2}}=3PQ=3{{P}^{2}}\] \[{{P}^{2}}={{P}^{2}}+{{Q}^{2}}+2PQ\,cos\theta \] \[\therefore \] \[3{{P}^{2}}={{P}^{2}}+{{P}^{2}}+2{{P}^{2}}cos\theta \] or \[3{{P}^{2}}-2{{P}^{2}}=2{{P}^{2}}cos\theta \] or \[{{P}^{2}}=2{{P}^{2}}cos\theta \] or \[1=2\text{ }cos\theta \] \[\therefore \] \[\cos \theta =\frac{1}{2}\] \[\theta =60{}^\circ =\frac{\pi }{3}\]
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