Vector Triple Product

and

(1318) |

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
lies along , and lies in the - plane. It follows that
,
, and
.
The vector
is directed along : *i.e.*,
. Hence,
lies in the - plane: *i.e.*,
.
This is the left-hand side of Equation (A.1317) in our convenient coordinate system. To evaluate the right-hand side,
we need
and
.
It follows that the right-hand side is

(1319) |

which proves the theorem.