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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

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`OA = hat i`
`OB = vec b_1 = -(cos 60^@)hat i + sin 60^@`
`OB = vec b_2= - cos 60^@ hat i - sin 60^@ hat j`
`vec a + vec b_1 = hat i - hat i/2 + sqrt3/2 hat j`
`= 1/2 hat i + sqrt3/2 hat j`
`vec a + vec b_2 = hat i - hat i/2 - sqrt3/2 hat j`
`= 1/2 hat i - sqrt3/2 hat j`
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