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

`pm ( hat a + hatb)/(2)`

B

`pm (hata + hatb)/(2 cos theta )`

C

`pm (hat a + hatb)/(2 cos theta //2)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
`(hata+ hat(b))/(|hata + hatb|)` will be teh besector of teh given vectors
`|hata+ hatb|^(2) = |hata|^(2) + |b| ^(2)+ 2 hata . hatb`
`1+1 + 2 cos theta`
` =2 (1 + cos theta)`
`=2xx2 cos ^(2) theta //2`
` = 4 cos ^(2) theta //2`
`|hata + hatb| =2 cos theta //2`
Since `pm ( hata + hatb)/(2 cos theta//2)`
Promotional Banner

Topper's Solved these Questions

  • JEE MAIN REVISON TEST-23

    VMC MODULES ENGLISH|Exercise MATHEMATICS (SECTION 2)|5 Videos

  • JEE Main Revision Test-9 | JEE-2020

    VMC MODULES ENGLISH|Exercise SECTION 2|5 Videos

  • MATRICES AND DETERMINANTS

    VMC MODULES ENGLISH|Exercise JEE ADVANCED ARCHIVE|78 Videos

Similar Questions

Explore conceptually related problems

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

If veca and vecb are unit vectors and theta is the angle between them then show that |veca-vecb|=2sin.(theta)/(2)

Let veca and vecb be two unit vectors and alpha be the angle between them, then veca + vecb is a unit vector , if alpha =

If veca and vecb are two vectors and angle between them is theta , then

If veca and vecb are unit vectors inclined at an angle theta , then the value of |veca-vecb| is

vecA and vecB are two vectors and theta is the angle between them, if |vecA xx vecB|=sqrt(3)(vecA.vecB) the value of theta is:-

If veca and vecb are unit vectors, then angle between veca and vecb for sqrt3 ​ veca − vec b to be unit vector is

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

If veca and vecb are unit vectors inclined to x-axis at angle 30^(@) and 120^(@) then |veca +vecb| equals

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