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. $\frac{1}{2} \left(\hat{n_{1}}\cdot\hat{n}_{2}\right)$
• C. $\frac{1}{2} \left(\left|\hat{n_{1}}+\hat{n_{2}}\right|\right)$
• D. $\frac{1}{2} \left(\left|\hat{n_{1}}\times\hat{n_{2}}\right|\right)$

Answer 1

Answer: (C)

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