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

Here `vec(A)xxvec(B)=ABsintheta` and `vec(A).vec(B)=ABcostheta`
Dividing `tantheta=(vec(A)xxvec(B))/(vec(A).vec(B))`
Also `|vec(A)xxvec(B)|=sqrt(3)vec(A).vec(B)`
`:.tantheta=(sqrt(3)vec(A).vec(B))/(vec(A).vec(B))=sqrt(3)` or `theta=60^@`
Let `vec(R )=vec(A)+vec(B)`
NOw by ||gm law, we have
`|vec(R)|=sqrt(A^(2)+B^(2)+2ABcostheta)`
`=sqrt(A^(2)+B^(2)+AB)`
`vec(A)+vec(B)=(A^(2)+B^(2)+AB)^(2)`