ABC is an equilateral triangle with `O` as its centre. `F_(1), F_(2)` and `F_(3)` represent three forces acting along the sides `AB, BC` and `AC` respectively. If the total about `O` is zero, then the magnitude of `F_(3)` is

Options

A. `((F_(1)+F_(2)))/(2)`
B. `(F_(1)-F_(2))`
C. `(F_(1)+F_(2))`
D. `2(F_(1)+F_(2))`

Answer

C

Explanation

For total torque about O to be zero

`F_(1)^(r)+F_(2^(r))-F_(3^(r))=0rArr phi_(3)=phi_(1)+phi_(2)rArr F_(3)=F_(1)+F_(2)`