A) \[\pi \]
B) \[\frac{\pi }{2}\]
C) \[\frac{\pi }{3}\]
D) \[\frac{\pi }{6}\]
E) \[\frac{7\pi }{3}\]
Correct Answer: A
Solution :
As, \[\mathbf{P}\times \mathbf{Q}=\mathbf{Q}\times \mathbf{P}\] \[(\mathbf{P}\times \mathbf{Q})-(\mathbf{Q}\times \mathbf{P})=0\] \[\Rightarrow \] \[(\mathbf{P}\times \mathbf{Q})-[-\,(\mathbf{P}\times \mathbf{Q})]=0\] \[\Rightarrow \] \[2\,(\mathbf{P}\times \mathbf{Q})=0\] \[\Rightarrow \] \[2PQ\sin \theta =0\] As \[|\mathbf{P}|\,\ne 0\]and \[|\mathbf{Q}|\,\ne 0\] This implies \[PQ\ne 0\] then \[\sin \theta =0\] \[\theta =0{}^\circ \,\text{or}\,\pi \]
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