Resultant of coplanar force system

SYSTEM OF COPLANAR CONCURRENT FORCES

When all the forces act in the same plane and their lines of action pass through a single common point, the system is called a coplanar concurrent force system.

To find resultant of coplanar concurrent forces :

Consider a given system of force shown in  the figure 

Force Resolution Table

The magnitude of the resultant force is: 

\(R = \sqrt{ \left(\sum F_x\right)^2 + \left(\sum F_y\right)^2 }\)

The direction of the resultant force is: 

\(\theta = \tan^{-1} \left( \frac{\sum F_y}{\sum F_x} \right)\)