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

Explanation

Let `hat(n)_(1)` and `hat(n)_(2)` are the two unit vectors,then sum is
`vec(n)_(s)=vec(n)_(1)+hat(n)_(2)`.
`rArrn_(s)^(2)=n_(1)^(2)+n_(2)^(2)+2n_(1)n_(2)cos theta=1+1+2 cos theta`
Since it is given that `vec(n)_(s)` is a unit vector, so `n_(s)=1`.
`:.1=1+1+2cos thetarArrcos theta=-1/2rArrtheta=120^(@)`
Now the diffrence vector is `vec(n)_(d)=vec(n)_(1)-vec(n)_(2)`
`rArrn_(d)^(2)=n_(1)^(2)+n_(2)^(2)-2n_(1)n_(2)cos theta=1+1-2cos(120^(@))=3`
`rArrn_(d)=sqrt(3)`