# ABC is an equilateral triangle with O as its centre. $\vec{F}_{1},\: \vec{F}_{2},\: \vec{F}_{3}$ represent three forces acting along the sides AB, BC and AC respectively. If the total torque about O is zero the magnitude of $\vec{F}_{3}$ Option 1) $F_{1}+F_{2}$ Option 2) $F_{1} - F_{2}$ Option 3) $\frac{F_{1}+F_{2}}{2}$ Option 4) $2(F_{1}+F_{2})$

As discussed in

Equilibrium -

$\sum \vec{F}=0$   Translational equilibrium

$\sum \vec{\tau }=0$     Rotational equilibrium

-

$F_{1}x+F_{2}x=F_{3}x$

$F_{3}=F_{1}+F_{2}$

Option 1)

$F_{1}+F_{2}$

This option is correct.

Option 2)

$F_{1} - F_{2}$

This option is incorrect.

Option 3)

$\frac{F_{1}+F_{2}}{2}$

This option is incorrect.

Option 4)

$2(F_{1}+F_{2})$

This option is incorrect.

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