Today I will talk about the scalar triple product of vectors.

Have a look!!

### Scalar triple product of vectors

###### Introduction

Suppose there are three vectors and .

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

In the same way, vector product of two vectors and is written as

I already know that scalar product of two vectors is a scalar quantity. Similarly, the vector product of two vectors is a vector quantity.

###### What is a scalar triple product?

Let

The scalar triple product of these three vectors is

Now is a vector since it is the vector product of two vectors and .

Therefore the formula for will be

#### Examples of scalar triple products

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 scalar triple product of ”

##### Solution

Here the three given vectors are

Now as per the formula for scalar triple product of vectors, the scalar triple product of vectors and will be

As a next step, now I’ll evaluate the determinant on the right-hand side to get the value of

Thus it will be

This is the answer to the problem.

Now I’ll go to the second example.

##### Example 2

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

##### Solution

Here the three given vectors are

Now as per the formula for scalar triple product of vectors, the scalar triple product of vectors and will be

As a next step, now I’ll evaluate the determinant on the right-hand side to get the value of

Thus it will be

This is the answer to the problem.

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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