Three point charges `q_(1)=q,q_(2)=q and q_(3)=Q` are placed at points having poisition vetors `vec(r_(1)),vec(r_(2))` and `(vecr_(1)+vecr_(2))` respectively. It is known that `|vecr_(1)|=|vecr_(2)|=vecr`. The net electrostatic force on `q_(3)` is `sqrt(3)` times the force applied by either of `q_(1)` or `q_(2)` on `q_(3)`. find `vecr_(1)*vecr_(2)`.

Answer

`(r^(2))/(2)`