A) \[\frac{\pi }{2}\]
B) 0
C) \[\frac{\pi }{4}\]
D) \[\frac{\pi }{3}\]
Correct Answer: A
Solution :
Let \[\overrightarrow{A}=\sqrt{3}(\overrightarrow{a}\times \overrightarrow{b}),\overrightarrow{B}=\overrightarrow{b}-(\overrightarrow{a}.\overrightarrow{b})\overrightarrow{a}\] Now, \[\overrightarrow{A}-\overrightarrow{B}=0\] \[\Rightarrow \]Angle between\[\overrightarrow{A}\]and\[\overrightarrow{B}\]is\[\frac{\pi }{2}\]. Alternative Method \[\overrightarrow{A}\]is lector\[\bot \]to plane of\[\overrightarrow{a}\]and\[\overrightarrow{b}\]while\[\overrightarrow{B}\]lies in he plane of\[\overrightarrow{a}\]and\[\overrightarrow{b}\]. \[\Rightarrow \] \[\overrightarrow{A}\bot \overrightarrow{B}\] \[\therefore \]Angle between\[\overrightarrow{A}\]and\[\overrightarrow{B}\]is\[\frac{\pi }{2}\].
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