If $\hat{a}, \hat{b}$ and $\hat{c}$ are unit vectors satisfying $\hat{a}-\sqrt{3} \hat{b}+\hat{c}=\overrightarrow{0}$, then the angle between the vectors $\hat{a}$ and $\hat{c}$ is :

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Aicharya · Accepted Answer

Let angle between $\hat{a}$ and $\hat{c}$ be $	heta$. Now, $\hat{a}-\sqrt{3} \hat{b}+\hat{c}=\overrightarrow{0}$ $ \begin{aligned} & \Rightarrow(\hat{a}+\hat{c})=\sqrt{3} \hat{b} \ & \Rightarrow(\hat{a}+\hat{c}) \cdot(\hat{a}+\hat{c})=3(\hat{b} \cdot \hat{b}) \ & \Rightarrow \hat{a} \cdot \hat{a}+\hat{a} \cdot \hat{c}+\hat{c} \cdot \hat{a}+\hat{c} \cdot \hat{c}=3 	imes 1 \ & \Rightarrow 1+2 \cos 	heta+1=3 \ & \Rightarrow \cos 	heta=\frac{1}{2} \Rightarrow 	heta=\frac{\pi}{3} \end{aligned} $

If $\hat{a}, \hat{b}$ and $\hat{c}$ are unit vectors satisfying $\hat{a}-\sqrt{3}…

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