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)/(sqrt(3)))^(1//2)`
B. `A + B`
C. `(A^(2) + B^(2) + sqrt(3) AB)^(1//2)`
D. `(A^(2) + B^(2) + AB)^(1//2)`

Answer

D

Explanation

`|vec(A) xx vec(B)| = sqrt(3) vec(A) . Vec(B)`
`AB sin theta = sqrt(3) AB cos theta`
`tan theta = sqrt(3) rArr theta = 60^(@)`
`|vec(A) + vec(B)| = sqrt(A^(2) + B^(2) + 2 AB cos 60^(@))`
` = (A^(2) + B^(2) + AB )^(1//2)`