When to use this calculator
The dot product combines vector magnitude and alignment. Its units depend on the units of the two input vectors.
Explore the coordinate & vector calculators for other questions in this topic. For a related calculation, use the Vector Magnitude Calculator: Find the length of a three-dimensional vector.
PUTTING IT INTO PRACTICE
Vector Dot Product: a worked example
The values below are an illustrative example, not a recommendation. Replace them with measurements or assumptions that match your question.
| Input | Example value |
|---|---|
| Vector A x | 1 |
| Vector A y | 2 |
| Vector A z | 3 |
| Vector B x | 4 |
| Vector B y | 5 |
| Vector B z | 6 |
| Result | 32 |
- Check the input labels and enter the example values above.
- Apply the relationship: Dot product = AxBx + AyBy + AzBz.
- The result is 32 , rounded for display.
How to interpret your result
A zero dot product indicates perpendicular nonzero vectors.
Keep coordinate units consistent along every axis. Distance is non-negative, while slope and dot product can have signs. A vertical line has undefined slope because the horizontal coordinate change is zero.
Frequently asked questions
Does a zero dot product always mean the vectors are perpendicular?
Two nonzero vectors with zero dot product are perpendicular. The zero vector needs separate treatment because it has no defined direction.
When is the vector dot product calculator useful?
The dot product combines vector magnitude and alignment. Its units depend on the units of the two input vectors.
How do I use the vector dot product calculator?
Enter vector a x, vector a y, vector a z, vector b x, vector b y, vector b z. The result updates automatically. Use the units shown beside each input; the example values illustrate the method.
Which formula does this calculator use?
Dot product = AxBx + AyBy + AzBz.
What should I check before using the result?
A zero dot product indicates perpendicular nonzero vectors.
How are results rounded?
Scalar numbers display up to six decimal places, with scientific notation for very large or small values. Text, fraction, date and schedule outputs use the format described on the tool. Intermediate calculations use JavaScript floating-point arithmetic. Keep sensible precision for your measurements.
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