# How to Calculate a Dot Product on a TI-84 Calculator

Given vector a = [a1, a2, a3] and vector b = [b1, b2, b3], the dot product of vector a and vector b, denoted as a · b, is given by:

a · b = a1 * b1 + a2 * b2 + a3 * b3

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 · b = 2*4 + 5*3 + 6*2

a · b = 8 + 15 + 12

a · b = 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, press 2nd then press STAT then scroll over to MATH 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 be 35. This matches the value that we calculated by hand.