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Basic Concepts Of Vector Part 7

Posted on - 04-01-2017

Math

IIT JEE

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, .

 
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