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To calculate a dot product on a TI-84 calculator, enter the vectors as lists, then press the MATH button and select the PROD command. Enter the list names of the two vectors, and the calculator will output the dot product. The dot product is a scalar number that is the result of multiplying the corresponding components of two vectors.
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:
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.