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, 
.
