# How to Apply a Vector Formula in Excel – 5 Examples

## What Is Vector Quantity?

A quantity with both direction and magnitude is called a Vector quantity.

The following dataset showcases vector data: Â Data A and Data B.

### Example 1 – Using an Addition Formula to Sum Two Vector Data

Steps:

• Enter the following formula in D5.
=B5:B10+C5:C10

• Since this is an ARRAY formula press CTRL+SHIFT+ENTER. (ForÂ Excel 365, press ENTER.)
• See the result in D5:D10.

### Example 2 – Use a Subtraction Formula to Deduct One Vector Data from Another

Steps:

• Enter the following formula in D5.
=B5:B10-C5:C10

• Since this is an ARRAY formula press CTRL+SHIFT+ENTER. (ForÂ Excel 365, press ENTER.)
• See the result in D5:D10.

### Example 3 – Using a Vector Dot Formula for Two Sets of Vector Data

#### 3.1. Generic Formula

Steps:

• Enter the following formula in D5.
=C5*B5

• Press ENTER.
• See the result in D5.
• Drag down the formula with the Fill Handle tool.

• This is the output.

• To find the sum of this multiplication: enter the following formula in D11.
=SUM(D5:D10)
• The SUM function sums the cell range.

• Press ENTER.
• See the result in D11.

#### 3.2. Applying the SUM Function

Use the SUM function to find the multiplication of a cell range.

Steps:

• Enter the following formula in C12.
=SUM(B5:B10*C5:C10)

• Press CTRL+SHIFT+ENTER.
• See the result in C5:C10.

#### 3.3. Combining the MMULT andÂ  the TRANSPOSE Functions

Use the MMULT and the TRANSPOSE functions in the vector formula to find the multiplication of vectors.

Steps:

• Enter the following formula in C12.
=MMULT(TRANSPOSE(B5:B10),(C5:C10))

Formula Breakdown

• The MMULT function returns the matrix product of two cell ranges.
• The TRANSPOSE function modifies the orientation of the cell range.
• TRANSPOSE(B5:B10)â†’ becomes
• Output: {3,5,7,9,11,13}
• MMULT(TRANSPOSE(B5:B10),(C5:C10) â†’ becomes
• MMULT({3,5,7,9,11,13}),(C5:C10))Â
• Output:Â  592
• Press ENTER.
• See the result in C12.

### Example 4 – Using a Vector Cross Formula for Two Sets of Vector Data

The following dataset showcases the value of IaI (value of the first vector), IbI (value of the second vector), and the angle between them Î¸ in degree.

• Convert the angle to Radians. and find the cross multiplication by using the formula a x b=IaI IbI SinÎ¸

Steps:

• Convert the Degree toÂ Radians: Enter the following formula in C8.

• Press ENTER.
• See the result in C8.

• To find the SinÎ¸, use the following formula in C9.
=SIN(C8)

The SIN function converts the Radian angle into the sin angle.

• Press ENTER.
• See the result in C9.

• To find the cross-product, enter the following formula in C10.
=C5*C6*C9

• Press ENTER.
• See the output in C10.

### Example 5 – Using a Vector Formula to Find Two Components Using Magnitude and Reference Angle of This Vector

In the image below the magnitude of a vector is 10, and the direction is 60Â°. You want to find X and Y.

X = 10 CosÎ¸
Y=10 SinÎ¸
Data was inserted in the dataset.

Steps:

• Convert Degrees to Radians, using the following formula in C7.

• Press ENTER.
• See the result in C8.

• To find X, enter the following formula in C8.
=C5*COS(C7)

• Press ENTER.
• See the result in C8.

• To find Y, enter the following formula in C9.
=C5*SIN(C7)

• See the outcome in C9.

This is the output.

## Vector Formula in Excel: Knowledge Hub

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Afia Kona

Afia Aziz Kona, a graduate of Civil Engineering from Khulna University of Engineering & Technology, Bangladesh, serves as a technical content creator in the ExcelDemy project. Possessing a passion for innovation and critical thinking, she actively embraces challenges. Beyond her engineering background, Afia exhibits a keen interest in Excel, having authored numerous articles on Excel & VBA-related issues to simplify the experience for users facing obstacles in Excel. Apart from creating Excel tutorials, she is also... Read Full Bio

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