What if one vector is zero?
The dot product returns zero and the angle is undefined because it depends on both magnitudes.
Step-by-step walkthrough
Dot Product Calculator Guide
Use this companion guide beside the interactive calculator to make sure you understand the “why” behind every click. Each section includes the classroom explanation, student-friendly language, and quick practice prompts.
Before you start
Collect the data points listed below and double-check their units. Keeping an organized “givens” list is one of the fastest ways to reduce math errors and impress exam graders.
- dot product
- scalar product
- angle
Detailed procedure
Step 1
Enter vector A and vector B using comma-separated components.
Step 2
Ensure both vectors share the same dimension.
Step 3
Review the dot product, magnitudes, and angle between the vectors.
Teaching & troubleshooting tips
Does the order matter?
No—the dot product is commutative, so swapping A and B produces the same result.