Vector Triple Product:
The
vector product of two vectors, one of which is itself the vector product
of two vectors, is a vector quantity called vector triple product.
It
is defined for three vectors as the vector . This vector being perpendicular to , is coplanar with .
i.e.
Take
the scalar product of this equation with a. We get.
0
=
&⇒
If
we choose the coordinate axes in such a way that
, it is easy to show that l = 1. Hence
In
general, ( Vector triple product is not associative
) .
if some or all of are
zero vectors or are collinear.
Example.1
Prove that
Solution
We have =
= = .
Example.2
Show that = 0.
Solution
L.H.S. = =0
Example.3
Prove that .
Solution
L.H.S. = =
= = R.H.S.
Example.4
If are
three unit vectors such that = , find the angles which makes with and
..
Solution
We are given that =
&⇒
&⇒ and
= 0
Hence the angle between is and that between, .