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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`
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