If the sum of two unit vectors is a unit vector, prove that the magnitude of their difference is `sqrt(3.)`

Options

A. `sqrt2`
B. `sqrt3`
C. `sqrt5`
D. 1

Answer

B

Explanation

(b): Let `hatn_(1)&hatn_(2)` represent two unit vectors and angle between them is `theta` .
`S^(2)=n_(1)^(2)+n_(1)^(2)+2n_(1)n_(2) cos theta`
`rArr 1=1+1+2 cos theta rArr cos theta =-1//2 rArr theta =120^(@)`
Magnitude of difference can be writen as follows:
`D^(2)=n_(1)^(2)+n_(2)^(2)-2n_(1)n_(2) cos theta`
`rArr D^(2) =1+1-2(-(1)/(2))=3`
`rArr D=sqrt3`
Hence, option (b) is correct.