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.
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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
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+a3b3.
- 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.
- 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.
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.