A) \[\frac{\pi }{6}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{2}\]
D) \[\frac{\pi }{4}\]
Correct Answer: B
Solution :
Let two vectors are \[\vec{a}\] and \[\vec{b}.\] then according to question \[|\vec{a}\times \vec{b}|=\sqrt{3}|\vec{a}.\vec{b}|\] \[\Rightarrow \]\[|\vec{a}|.|\vec{b}|sin\theta =\sqrt{3}|\vec{a}||\vec{b}|cos\theta \] \[\Rightarrow \]\[\tan \theta =\sqrt{3}-\tan \frac{\pi }{3}\] \[\Rightarrow \]\[\theta =\frac{\pi }{3}.\]
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