and

(52) |

Let us try to prove the first of the above theorems. The left-hand side and the
right-hand side are both proper vectors, so if we can prove this result in one particular
coordinate system then it must be true in general. Let us take convenient axes such that the
-axis lies along , and lies in the - plane. It follows that
,
, and
.
The vector
is directed along the -axis:
. It follows that
lies in the - plane:
.
This is the left-hand side of Eq. (51) in our convenient axes. To evaluate the right-hand side,
we need
and
.
It follows that the right-hand side is

(53) |

which proves the theorem.