If unit vectors $\hat{A}$ and $\hat{B}$ are inclined at an angle $ heta$, then $|\hat{A}-\hat{B}|$

Question

If unit vectors $\hat{A}$ and $\hat{B}$ are inclined at an angle $	heta$, then $|\hat{A}-\hat{B}|$ is

Professor PC Thomas Classes · Answer

(a) : $|\hat{A}-\hat{B}|^2=|\hat{A}|^2+|\hat{B}|^2-2 \hat{A} \hat{B} \cos 	heta$ $ \  \begin{aligned} & =2-2 \cos 	heta=2(1-\cos 	heta) \ & =2\left(2 \sin ^2 \frac{	heta}{2}ight)=4 \sin ^2 \frac{	heta}{2} 	ext { or }|\hat{A}-\hat{B}|=2 \sin \frac{	heta}{2} \end{aligned} $ \ $ (\because|\hat{A}|=|\hat{B}|=1) $