Question

If ${\hat{n}}_1,{\hat{n}}_2$ are two unit vectors and $\theta$ is the angle between them, then $cos\theta /2=$

• A. $\frac{1}{2}\left|{\hat{n}}_1-{\hat{n}}_2\right|$
• B. $\frac{1}{2}\left(\widehat{n_1}\cdot {\hat{n}}_2\right)$
• C. $\frac{1}{2}\left(\left|\widehat{n_1}+\widehat{n_2}\right|\right)$
• D. $\frac{1}{2}\left(\left|\widehat{n_1}\times \widehat{n_2}\right|\right)$

Answer 1

Answer: (C)

Since, ${\left|{\hat{n}}_1+{\hat{n}}_2\right|}^2$
$={\left|{\hat{n}}_1\right|}^2+{\left|{\hat{n}}_2\right|}^2+2\left|{\hat{n}}_1\right|\left|{\hat{n}}_2\right|cos\theta =2\left(1+cos\theta \right)=4co{s}^2\theta /2$
$\therefore cos\theta /2=\frac{1}{2}\left|{\hat{n}}_1+{\hat{n}}_2\right|$