Direction Cosines Model
To aid in perception of the components of a three-dimensional vector.
Direction cosines model, as photographed.
Emphasize that the angle between the vector and any axis is not the same as the angle between the axis and the projection of the vector onto a plane defined by two axes.
An arbitrary vector in three-dimensional space is shown along with projections along the three orthogonal axes. Observe how the angles alpha, beta, gamma are defined.