For scientific analysis we may have to calculate **vector multiplication**. We can use the** Excel spreadsheet **for this multiplication. In this article, we will show you how you can perform this **Vector Multiplication** in an Excel spreadsheet.

## Download Practice Workbook

You can download and practice this workbook.

## Basics of Vector Multiplication

Vector quantity is something that represents both the magnitudes and direction. We can multiply two vector quantities in two ways.

**Dot or Scalar Product**

Dot product returns the multiplication between a vector’s magnitude and the scalar projection of another vector in the direction of the first vector. It doesn’t give us any direction. So, dot product results in scalar output. That’s why it is also called scalar multiplication.

Let’s take two vectors **A̅** and **B̅**.

**A̅ = a _{1}î+a_{2}ĵ+a_{3}K̂**

**B̅ = b _{1}î+b_{2}ĵ+b_{3}K̂**

Their dot product will be

**A̅.B̅= a _{1}b_{1}+a_{2}b_{2}+a_{3}b_{3}**

**Cross Product**

Cross product between two vectors gives direction along with magnitude. The magnitude of cross product means the area of a parallelogram which is created by those two vectors. It is also known as vector multiplication.

For the same two vector **A̅** and **B̅,**

**A̅ = a _{1}î+a_{2}ĵ+a_{3}K̂**

**B̅ = b _{1}î+b_{2}ĵ+b_{3}K̂**

The formula for cross multiplication will be

**A̅ × B̅ = (a _{2}b_{3}-a_{3}b_{2})î+(a_{3}b_{1}-a_{1}b_{3})ĵ+(a_{1}b_{2}-a_{2}b_{1})K̂**

## 2 Examples for Vector Multiplication in Excel

### 1. Vector Multiplication with Dot Product

We need two vector values and then have to find the value of **a**_{1}**b**_{1}**+a**_{2}**b**_{2}**+a**_{3}**b**_{3}_{.}

**Steps:**

- So, let’s take two vectors
**a**and**b**. - Separate their coefficients in two different rows like the image below.

- Now, write the following formula in
**C8**and press**ENTER**.

`=C5*C6+D5*D6+E5*E6`

This formula returns the value of dot product of two vectors where the values in column **C**,** D** and **E** represent the coefficients of those two vectors.

So, you will get the value of dot multiplication in **C8** which is **32**.

### 2. Vector Multiplication with Cross Product

For this multiplication, we have to include the unit vectors **î**,** ĵ** and** K̂**. We can use the **CONCATENATE** function for this purpose.

We have taken the same **a **and **b **vectors for our cross product.

**Steps:**

- First, we have to find out the value of
**(a**_{2}**b**_{3}**-a**_{3}**b**_{2}**)**,**(a**_{3}**b**_{1}**-a**_{1}**b**_{3}**)**and**(a**_{1}**b**_{2}**-a**_{2}**b**_{1}**)**. - So, create a separate table to calculate these values.

- Write the following formula in
**B9**and press**ENTER**.

`=D5*E6-E5*D6`

This formula gives the value of coefficient **(a**_{2}**b**_{3}**-a**_{3}**b**_{2}**) **where the column **D** and **E** represent the coefficients of two vectors.

- Thereby, we get the value of
**(a**_{2}**b**_{3}**-a**_{3}**b**_{2}**)**.

- Now, for the value of
**(a**_{3}**b**_{1}**-a**_{1}**b**_{3}**)**write the following formula in**C9**and press**ENTER**.

`=E5*C6-C5*E6`

The formula returns the value of coefficient **(a**_{3}**b**_{1}**-a**_{1}**b**_{3}**) **where column **C **and** E** represent the coefficients of two vectors.

- For the last value
**(a**_{1}**b**_{2}**-a**_{2}**b**_{1}**)**, write the following formula in**D9**and press**ENTER**.

`=C5*D6-D5*C6`

This formula returns the value of coefficient **(a**_{1}**b**_{2}**-a**_{2}**b**_{1}**) **where column **C **and** D** represent the coefficients of two vectors

And, now we are ready for the last bit.

- For the complete result write the following formula in
**C11**and press**ENTER**.

`=CONCATENATE(B9,C4,"+(",C9,")",D4,"+(",D9,")",E4)`

The formula joins texts from two different cells and then adds these joined texts together.

Thereby, we have got the result for cross multiplication.

## How to Create Vector Multiplication Calculator in Excel

You can download the practice workbook and there is this vector multiplication calculator. You have to insert the coefficient of vectors and this calculator will give you the value for both dot and cross product.

## Conclusion

Thank you for making it this far. We have shown you two types of **vector multiplication** in Excel. We hope you find the content of this article useful. If there are further queries or suggestions feel free to mention them in the comment section. Have a nice day.