If the sum of two unit vectors is a unit vector, then magnitude of difference is-

Options

A. `sqrt(2)`
B. `sqrt(3)`
C. `(1)/sqrt(2)`
D. `sqrt(5)`

Answer

B

Explanation

`|hatn_(2)+hatn_(2)|=1`
`sqrt(1^(2)+1^(2)+2 cos theta)=12+2 cos theta=1`
`rArr costheta=(-1)/(2)rArrtheta=120^(@)`
`|hatn_(1)-hatn_(2)|=sqrt(1^(2)+1^(2)-2xx1xxa cos 120^(@))=sqrt(3)`