Resultant of Coplanar Concurrent Forces:

The technique of resolution of a force may be utilized to determine the resultant of coplanar concurrent forces. If 'n' concurrent forces F₁, F₂, F₃, . . . , F_n are acting at a specific point in a body then each force may be resolved into two mutually perpendicular directions. Therefore, we get '2n' components. Each set of 2n components (n components along with x-direction; and n components along with y-direction) acts only in one direction. Thus, we may algebraically add all of these components to get the components of the resultant.

R_x  = ∑ F_ix

 = F_1x  + F_{2 x}  + F_{3 x}  + . . . + F_nx

Ry  = ∑ F_iy

= F_{1 y}  + F_{2 y}  + F_{3 y}  + . . . + F_ny

At last, combining these components R_x and R_y, vectorially, we obtain the resultant R.

Therefore,

 R¯ = R¯_x i¯ + R¯ _y j¯

and

θ = tan ^-1   (R_y / R_x)

Here, θ is the angle of inclination of the resultant R¯ w.r.t. positive x-axis.