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

Options

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

Answer

B

Explanation

Vector in the direction of angular bisector of a and b is `(a+b)/(2)`.
Unit vector in this direction is `(a+b)/(|a+b|)`

From the figure, position vector of E is `(a+b)/(2)`.
Now is triangle AEB, AE=`AB"cos"(theta)/(2)`
`implies|(a+b)/(2)|="cos"(theta)/(2)`.
Hence, unit vector along the bisector is `(a+b)/(2cos(theta//2))`.