*45*

Given vector *a* = [a_{1}, a_{2}, a_{3}] and vector *b* = [b_{1}, b_{2}, b_{3}], theÂ **dot product**Â of vector a and vector b, denoted asÂ **a Â· b**, is given by:

**a Â· b**Â = a_{1}Â * b_{1}Â + a_{2}Â * b_{2}Â + a_{3}Â * b_{3}

For example, if *a* = [2, 5, 6] and *b* = [4, 3, 2], then the dot product of *a* and *b* would be equal to:

**a Â· b =Â **2*4 + 5*3 + 6*2

**a Â· b =Â **8 + 15 + 12

**a Â· b =Â **35

We can use the following syntax to calculate the dot product of two vectors on a TI-84 calculator:

sum({2, 5, 6}*{4, 3, 2})

The following step-by-step example shows how to use this syntax in practice.

**Example: Calculate Dot Product on TI-84 Calculator**

Use the following steps to calculate the dot product between two vectors:

**Step 1: Enter the sum( command.**

First,Â press 2nd then press STAT then scroll over to MATHÂ and press sum:

**Step 2: Enter the left curly brace.**

Next, press 2nd then press ( to enter the first curly brace:

**Step 3: Enter the Data**

Next, enter the following values for each vector:

- Vector a: 2, 5, 6
- Vector b: 4, 3, 2

Be sure to include a multiplication sign between the two vectors and close off the end of the sum() command with a parenthesis on the right. Then press ENTER:

The dot product turns out to beÂ **35**. This matches the value that we calculated by hand.

**Additional Resources**

How to Calculate the Dot Product in Excel

How to Calculate the Dot Product in Google Sheets

How to Calculate the Dot Product in R