Home
Class 12
MATHS
Let vec a= hat i be a vector which makes...

Let `vec a= hat i` be a vector which makes an angle of `120^@` with a unit vector `vec b` in XY plane. then the unit vector `(vec a+ vec b)` is

A

`-(1)/(2)hati+(sqrt(3))/(2)hatj`

B

`-(sqrt(3))/(2)hati+(1)/(2)hatj`

C

`(1)/(2)hati+(sqrt(3))/(2)hatj`

D

`(sqrt(3))/(2)hati-(1)/(2)hatj`

Text Solution

Verified by Experts

The correct Answer is:
C
`b=cos120^(@)hati+sin120^(@)hatj`
or `b=-(1)/(2)hati+(sqrt(3))/(2)hatj`
therefore, `a+b=hati-(1)/(2)hati+(sqrt(3))/(2)hatj=(1)/(2)hati+(sqrt(3))/(2)hatj`
Promotional Banner

Similar Questions

Explore conceptually related problems

Projection vectors vec a on vec b is

The unit vector bisecting vec(OY) and vec(OZ) is

Statement 1: If vec ua n d vec v are unit vectors inclined at an angle alphaa n d vec x is a unit vector bisecting the angle between them, then vec x=( vec u+ vec v)//(2sin(alpha//2)dot Statement 2: If "Delta"A B C is an isosceles triangle with A B=A C=1, then the vector representing the bisector of angel A is given by vec A D=( vec A B+ vec A C)//2.

If vec a and vec b are unit vectors |vec a xx vec b| =1 then the angle between vec a and vec b is

The unit vector which is orthogonal to the vector vec a = 3i+2j+6k and is coplanar with the vectors vec b = 2i+j+k and vec c = i-j+k is

If vec a and vec b are unit vectors and theta is the angle between them, then |vec a + vec b| =

If vec a and vec b are unit vectors, then angle between vec a and vec b for sqrt(3)vec a - vec b to be unit vector is

Let the unit vectors vec a and vec b be perpendicular to each other and the unit vector vec c be inclined at an angle theta to both vec a and vec b . If vec c = x vec a + y vec b + z (vec a xx vec b) then,