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If veca and vecb are two unit vectors an...

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

A

`(a-b)/(2cos(theta//2))`

B

`(a+b)/(2cos(theta//2))`

C

`(a-b)/(cos(theta//2))`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
B
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))`.
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