ES40 Vector Resolution  Direction Cosines 

A vector may also be specified by magnitude and the angle it makes with the three coordinate axes. This is indicated in the three figures we see here. 
The components, F_{x}, F_{y}, and F_{z} may be determined. 
A force in three dimensions may be specified by its magnitude and
either direction cosines, or Euler angles. If a force is specified in Cartesian coordinates, it may be given as the magnitude of the components and unit direction vectors , , . 