Resultant of Concurrent Force System

    $R_x = \Sigma F_x = F_ + F_ + F_ + . $
    The x-component of the resultant is equal to the summation of forces in the x-direction.

Note that according to the type of force system, one or two or three of the equations above will be used in finding the resultant.

Resultant of Coplanar Concurrent Force System
The line of action of each forces in coplanar concurrent force system are on the same plane. All of these forces meet at a common point, thus concurrent. In x-y plane, the resultant can be found by the following formulas:

002-resultant-coplanar-concurrent-forces.jpg

$R_x = \Sigma F_x$

Resultant of Spatial Concurrent Force System
Spatial concurrent forces (forces in 3-dimensional space) meet at a common point but do not lie in a single plane. The resultant can be found as follows:

Resultant of concurrent forces in space

$R_x = \Sigma F_x$ $\cos \theta_x = \dfrac$

$\cos \theta_y = \dfrac$

$\cos \theta_z = \dfrac$

Vector Notation of the Resultant
$ = \Sigma $

$ = R_x + R_y + R_z$

Where
$R_x = \Sigma F_x$