Moment of Coplanar Forces:

Assume F₁, F₂ and F₃ be the three coplanar forces acting on a body and consider θ₁, θ₂, and θ₃ be the angles which these forces make with positive x-axis as illustrated in Figure.

Now, the magnitude & direction of resultant R may be found out easily by resolving all the forces horizontally and vertically as already known.

Assume the resultant R makes an angle θ with positive x axis as illustrated in Figure.

Now, through computation of moment of forces, the position of resultant force R may be ascertained.

To find out the point of application of the resultant, allow it cut the horizontal axis XOX at A at a perpendicular distance d from O as illustrated in Figure. For point O in Figure, assume the algebraic sum of the moments of the given forces around O be given by ΣM_o anticlockwise.

Then,      ∑ M _o  = F₁ d₁  + F₂ d ₂  + F₃ d₃

Now, through applying Varignon's theorem, the position of resultant R shall be such that the moment of R around point O, is equal to Σ M_o, and the direction of the moment because of R about moment centre O should be the same as Σ M_o because of the given system of forces.

Therefore,       R × d = Σ M_o

The distance d (perpendicular from O on R) is calculated from the above relation and R, whose magnitude & direction have already been find out earlier, is now fully located.