Home
Class 12
MATHS
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))`.
Promotional Banner

Similar Questions

Explore conceptually related problems

If hatl and hatm are unit vectors and theta is the angle between then theta is given by

If veca and vecb are unit vectors and theta is the angle between veca and vecb , then sin.(theta)/(2) is

Let vec a . vec b be two unit vectors and theta is the angle between them. Then vec a + vec b is a unit vector if

If veca and vec b are unit vectors, then what is the angle between veca and vecb for sqrt3 veva - vecb to be a unit vectors ?

If veca and vecb are two unit vectors such that veca + 2 vecb and 5 veca - 4 vecb are perpendicular to each other, then the angle between veca and vecb is :

If veca,vecb and vecc are unit vectors such that veca+vecb+vecc=vec0 then angle between veca and vecb is

If veca and vecb are two unit vectors, then the vector (veca + vecb) xx (veca xx vecb) is parallel to the vector :

Find the angle between the two vectors veca and vecb such that |veca|=1,|vecb|=1 and veca.vecb=1

If |veca+ vecb| lt | veca- vecb| , then the angle between veca and vecb can lie in the interval