A) \[\frac{\pi }{3}\]
B) \[\frac{\pi }{4}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{\pi }{2}\]
Correct Answer: C
Solution :
\[|a|=1,|b|=1,[a\,b\,a\times b]=\frac{1}{4}\] \[\Rightarrow \] \[(a\times b).(a\times b)=\frac{1}{4}\] \[\Rightarrow \] \[{{(|a||b|\sin \theta )}^{2}}=\frac{1}{4}\] \[\Rightarrow \] \[{{\sin }^{2}}\theta =\frac{1}{4}\] \[\Rightarrow \] \[\sin \theta =\frac{1}{2}\Rightarrow \theta =\frac{\pi }{6}\]
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