Driedimensionaal krachtsysteem

A boat is tied to a dock at the origin of a three-dimensional system. The tension force in the rope can be determined by resolving into its components in a three-dimensional space.

Consider the plane OLMN that contains the force vector and passes through the vertical z-axis.

This force makes an angle: theta with the z-axis and the plane OLMN is at an angle phi to the x-axis.

The vertical and horizontal components of the force in the plane OLMN can be expressed as the trigonometric functions of angle theta.

However, the resolved horizontal component can be further resolved to give the scalar components along the 'x' and 'y' axes in terms of angle phi.

Substituting for the horizontal component gives the x and y components in terms of angles theta and phi.

The magnitude of F_h can be obtained using the Pythagorean theorem in triangle ONP. Similarly, using Pythagoras in triangle OLM . expresses the magnitude of force 'F' in terms of its components along the x, y and z axes.