A) \[\frac{\pi }{4}\]
B) \[\frac{\pi }{3}\]
C) \[\frac{\pi }{6}\]
D) \[\frac{\pi }{2}\]
Correct Answer: B
Solution :
Let angle between \[\hat{a}\]and \[\hat{c}\] be \[\theta .\] Now, \[\hat{a}-\sqrt{3}\hat{b}+\hat{c}=\vec{0}\] \[\Rightarrow \]\[(\hat{a}+\hat{c})=\sqrt{3}\hat{b}\] \[\Rightarrow \]\[=(\hat{a}+\hat{c}).(\hat{a}+\hat{c})=3(\hat{b}.\hat{b})\] \[\Rightarrow \]\[\hat{a}.\hat{a}+\hat{a}.\hat{c}+\hat{c}.\hat{a}+\hat{c}.\hat{c}=3\times 1\] \[\Rightarrow \]\[1+2\cos \theta +1=3\] \[\Rightarrow \]\[\cos \theta =\frac{1}{2}\Rightarrow \theta =\frac{\pi }{3}\]
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