ES20 Vector Resolution in Three Dimensions 
A vector in three dimensions may be defined in terms of the angle it makes with the vertical (y) axis and the angle a vertical plane passed through it makes with the xaxis. These angles are known as the Euler angles. 

The y component, A_{y}, and the component in the xy plane,
A_{h}, may be found as shown here.

This is shown graphically.


The horizontal component, A_{h}, may be broken into x and z components. 
This is shown graphically. 
The reverse, given a vector in Cartesian components to find the magnitude and orientation in space, may also be performed. For example, consider the diagram here. 
… 
The magnitude and direction can be determined as shown here. 