यदि `|vec(A) xx vec(B)| = sqrt(3) vec(A).vec(B)`, तब `|vec(A) + vec(B)|` का मान है

Options

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

Answer

A

Explanation

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