If `|vec(A)xxvec(B)|=sqrt(3)vec(A).vec(B)`, then the value of `|vec(A)+vec(B)|` is

Options

A. `(A^(2) + B^(2) + (AB)/(sqrt3))^(1//2)`
B. `A+ B`
C. `(A^(2) + B^(2) + sqrt3 AB)^(1//2)`
D. `(A^(2) + B^(2) + AB)^(1//2)`

Answer

D

Explanation

`|vec(A) xx vec(B)|= sqrt3 vec(A).vec(B)`
`rArr AB sin theta= sqrt3AB cos theta`
`rArr tan theta= sqrt3 rArr theta= 60^(@)`
`|vec(A) + vec(B)| = sqrt(A^(2) + B^(2) + 2AB cos theta)= sqrt(A^(2) + B^(2) + AB)`