The classical definition of angular momentum is a pseudo-vector, which can be separated into its 3 components in Cartesian coordinates as follows:

If and are two vectors

where is the component of in the -direction and are unit vectors in the directions.

The cross product of the two vectors is:

Since

Comparing eq59a and eq69,

and

, and are the classical orbital angular momenta about the -axis, -axis and -axis respectively. Since the magnitude of a vector is , we have or simply

In other words, is square of the magnitude of the vector . The significance of will be explored in subsequent articles.

###### Question

Show that .

###### Answer

From eq59a,

Hence,