Question

If $\overline{a}$ and $\overline{b}$ are two unit vectors and $\theta$ is the angle between them, then the unit vector along their angular bisector is

• A. $\frac{\overline{a}-\overline{b}}{2\cos \frac{\theta }{2}}$
• B. $\frac{\overline{a}+\overline{b}}{2\cos \frac{\theta }{2}}$
• C. $\frac{\overline{a}-\overline{b}}{\cos \frac{\theta }{2}}$
• D. $\frac{\overline{a}+\overline{b}}{\cos \frac{\theta }{2}}$

Answer 1

Answer: (B)

$\frac{\overline{a}+\overline{b}}{2\cos \frac{\theta }{2}}$

Vector in the direction of angle bisector of $\overline{a}$ and $\overline{b}$ is $\frac{\overline{a}+\overline{b}}{2}$
It has the magnitude $\cos \frac{\theta }{2}$
$\therefore$ Unit vector along direction of angular bisector $\frac{\overline{a}+\overline{b}}{2\cos \frac{\theta }{2}}$