If `|AxxB| = sqrt3 A.B,` then the value of |A+B| is

Options

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

Answer

A

Explanation

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