scalar triple product of vectors. Today I will talk about the scalar triple product of vectors. Have a look!!

Want to know more about the triple product of vectors? Check out:

There’s also more in the product of vectors such as:

* scalar and vector products of two vectors*.

Scalar triple product_compressed

**The scalar triple product of vectors**

**Introduction**

Suppose there are three vectors and .

Earlier, I have talked about the * 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 the 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**

Now here the three given vectors are

and

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

Next, I’ll evaluate the determinant on the right-hand side to get the value of

Thus it will be

Then I’ll simplify it to get

which gives

Again I’ll simplify it a bit more to get

And this is the answer to the given example.

Next, I’ll give one more example.

**Example 2**

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

**Solution**

Now here the three given vectors are

and

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

Next, I’ll evaluate the determinant on the right-hand side to get the value of . Thus it will be

And this is the answer to the given example.

Dear friends, this is the end of 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!!

Aspriha says

Thanks a lot. Have a good time too.