1.

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

Answer»

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

SOLUTION :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)`


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