If `vec a` and `vec b` are two unit vectors and `theta` is the angle between them, then the unit vector along the angular bisector of `vec a` and `vec b` will be given by

Options

A. `(veca -vecb)/(2cos(theta//2))`
B. `(veca+ vecb)/(2cos(theta//2))`
C. `(veca-vecb)/(cos(theta//2))`
D. none of these

Answer

B

Explanation

Vector in the direction of angular bisector of `veca and vecb` is `(veca+vecb)/(2)`.
Unit vector in the direction is `(veca+vecb)/(|veca+vecb|)`.

From the figure, position vector of E is `(veca+vecb)/(2)`
Now in triangle AEB, AE = AB`cos""(theta)/(2)`
`rArr |(veca+vecb)/(2)|= cos ""(theta)/(2)`
Hence, unit vector along the bisector is `(veca + vecb)/(2cos (theta//2))`