Resultant of a force system is a force or a couple that will have the same effect to the body, both in translation and rotation, if all the forces are removed and replaced by the resultant.

The equation involving the resultant of force system are the following

The x-component of the resultant is equal to the summation of forces in the x-direction.

The y-component of the resultant is equal to the summation of forces in the y-direction.

The z-component of the resultant is equal to the summation of forces in the z-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:

**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:

Direction Cosines

**Vector Notation of the Resultant**

Where

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