If sum of two unit vectors is a unit vector; prove that the magnitude of their difference is `sqrt3`

Options

A. `sqrt(2)`
B. `sqrt(3)`
C. 1
D. none of these

Answer

B

Explanation

From the figure, `vec(OA)=hata, vec(OC)=hatb`
`vec(OA) + vec(OC) = vec(OB)=hata + hatb`
Now `|hata+hatb|=1`
`therefore DeltaQAB` is equilateral
`therefore` In `DeltaAOC, cos 120^(@)=(OA^(2) + OC^(2)-AC^(2))/(2OA.OC)`
`therefore -1/2=(1+1-AC^(2))/(2)`
`therefore AC=|veca-vecb|=sqrt(3)`