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

Options

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`

Answer

C

Explanation

`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`