Determine the magnitude and direction of the resultant of six concurrent forces applied to the center of a regular hexagon, as shown in the diagram.

The problem asks to determine the magnitude and direction of the resultant of six concurrent forces applied to the center of a regular hexagon. The diagram shows the forces pointing from the vertices towards the center. We will use this visual representation for the direction of the forces.

A regular hexagon has its vertices $60^\circ$ apart. Let's define the angles for the forces, assuming the positive x-axis points to the right and the center of the hexagon is the origin. The forces are pointing from the vertices towards the center.

The forces and their angles (measured counter-clockwise from the positive x-axis) are:

• $F_{11N} = 11\, \text{N}$ (from the left vertex, which is at $180^\circ$):