Hi friends, today I will talk about the vector triple product.

Have a look!!

### Vector triple product

###### Introduction

Suppose there are three vectors and .

Earlier, I have talked about vector product of two vectors. The vector product of two vectors and is written as

I already know that the vector product of two vectors is a vector quantity. Now, what happens with vector products if there are three vectors instead of two?

Well, then the vector product of three vectors is called ‘vector triple product’.

###### What is a vector triple product?

Let

The vector triple product of these three vectors is Like any vector product of two vectors, vector triple product is also a vector.

Now I will show some examples on vector triple product.

#### Examples of vector triple product

Note: None of these examples are mine. I have chosen these from some book or books. I have also given the due reference at the end of the post.

So here is the first example.

##### Example 1

According to Stroud and Booth (2011)* “Find the vector triple product of the following: ”

##### Solution

Here the given vectors and are

First of all, I will get That means vector product of two vectors and

Thus it will be

Now I will simplify the right hand side of the determinant to get the value of

Therefore I can say

Next I will get Thus it will be

Now I will simplify the right hand side of the determinant to get the value of

Therefore I can say

Hence I can conclude that the vector triple product of is

This is the answer to this example.

Now I will move to the next problem.

##### Example 2

According to Stroud and Booth (2011)* “Find the vector triple product of the following: ”

##### Solution

Here the given vectors and are

First of all, I will get That means vector product of two vectors and

Thus it will be

Now I will simplify the right hand side of the determinant to get the value of

Therefore I can say

Next I will get Thus it will be

Now I will simplify the right hand side of the determinant to get the value of

Therefore I can say

Hence I can conclude that the vector triple product of is

This is the answer to this example.

Dear friends, this is the end of my today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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