How to Calculate Vector Multiplication in Excel (2 Useful Examples)

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 = a₁î+a₂ĵ+a₃K̂

B̅ = b₁î+b₂ĵ+b₃K̂

Their dot product will be

A̅.B̅= a₁b₁+a₂b₂+a₃b₃

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 = a₁î+a₂ĵ+a₃K̂

B̅ = b₁î+b₂ĵ+b₃K̂

The formula for cross multiplication will be

A̅ × B̅ = (a₂b₃-a₃b₂)î+(a₃b₁-a₁b₃)ĵ+(a₁b₂-a₂b₁)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 a₁b₁+a₂b₂+a₃b_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.

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.

Read More: How to Apply Vector Formula in Excel (5 Suitable Examples)

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 (a₂b₃-a₃b₂), (a₃b₁-a₁b₃) and (a₁b₂-a₂b₁).
• So, create a separate table to calculate these values.

• Write the following formula in B9 and press ENTER.

This formula gives the value of coefficient (a₂b₃-a₃b₂) where the column D and E represent the coefficients of two vectors.

• Thereby, we get the value of (a₂b₃-a₃b₂).

• Now, for the value of (a₃b₁-a₁b₃) write the following formula in C9 and press ENTER.

The formula returns the value of coefficient (a₃b₁-a₁b₃) where column C and E represent the coefficients of two vectors.

• For the last value (a₁b₂-a₂b₁), write the following formula in D9 and press ENTER.

This formula returns the value of coefficient (a₁b₂-a₂b₁) 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.

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

Thereby, we have got the result for cross multiplication.

Read More: How to Calculate Eigenvalues and Eigenvectors in Excel

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.

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