If the sum of two unit vectors is a unit vector,then find the magnitude of their differences.

Options

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

Answer

B

Explanation

`vec(A) = 1 , vec(B) = 1, vec( R ) = 1`
`R^(2) = A^(2) + B^(2) + 2 AB cos theta`
`cos theta = -(1)/(@) rArr theta = 120^(@)`
`vec(R ') = vec(A) - vec(B)`,
`|vec(R' )| = R' = sqrt((1)^(2) + (1)^(2) + 2 . 1.1 cos 60^(@))`
`= sqrt(3)`