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

Options

A. `sqrt2`
B. `sqrt3`
C. `(1)/(sqrt2)`
D. `sqrt5`

Answer

2

Explanation

`|hatn_1+ hatn_2| = 1`
`sqrt(1^(2)+ 1^(2) + 2cos theta)=1 rArr 2+2 cos theta = 1`
`rArr cos theta = (-1)/(2) rArr theta = 120^(@)`
`|hatn_1 - hatn_2| = sqrt(1^(2)+ 1^(2) - 2xx1xx1 cos 120^(@)) = sqrt3`