## 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**. (For**Â 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**. (For**Â 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**.

`=RADIANS(C7)`

**The RADIANS function** converts the **degree** into **radians**.

- 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
, enter the following formula in*cross-product***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**.

`=RADIANS(C6)`

- 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.

## Practice Section

Download the following Excel file and practice.

**Download Practice Workbook**

Download the Excel file and practice.

## Vector Formula in Excel: Knowledge Hub

- How to Calculate Vector Multiplication in Excel
- How to Calculate Eigenvectors in Excel
- How to Calculate Eigenvalues and Eigenvectors in Excel

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