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Q.
If $\hat{a}, \hat{b}$ and $\hat{c}$ are unit vectors satisfying $\hat{a}-\sqrt{3} \hat{b}+\hat{c}={0}$, then the angle between the vectors $\hat{a}$ and $\hat{c}$ is
Vector Algebra
Solution:
$|\hat{a}+\hat{c}|^2=|\sqrt{3} \hat{b}|^2 $
$1+1+2 \cos \theta=3$
where $\theta=$ angle between $\hat{a}$ and $\hat{c}$
$\Rightarrow \cos \theta=\frac{1}{2}$
So, $\theta=\frac{\pi}{3}$