A) \[\frac{\pi }{2}\]
B) \[\frac{\pi }{4}\]
C) \[0\]
D) \[\frac{\pi }{3}\]
Correct Answer: A
Solution :
Let\[\mathbf{A}=\sqrt{3}(\mathbf{a}\times \mathbf{b})\]and\[\mathbf{B}=\mathbf{b}-(\mathbf{a}\cdot \mathbf{b})\mathbf{a}\] A is the vector perpendicular to the plane of\[\mathbf{a},\,\,\mathbf{b}\]. B is the vector lies in the plane of\[\mathbf{a},\,\,\mathbf{b}\]. \[\therefore \] \[\mathbf{A}\cdot \mathbf{B}=0\] or the angle between them is\[\frac{\pi }{2}\].
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