Formula and method
The dot product sums corresponding component products. For nonzero vectors, cos θ = (a·b)/(|a||b|).
Worked example
Vectors (1, 0, 0) and (0, 1, 0) have dot product 0, angle 90° and cross product (0, 0, 1).
Vector Calculator
Calculate dot product, sum, difference and angle for matching vectors, plus the cross product for three-dimensional vectors.
Printed from Calxy · https://www.calxy.net/math/vector-calculator
Dot product32.0000
Dot product
32.0000
- Vector sum5, 7, 9
- Vector difference (first − second)-3, -3, -3
- Angle between vectors12.9332 degrees
- Cross product (first × second)-3, 6, -3
Vectors must be expressed in the same orthonormal coordinate system and compatible units.
How this was calculated
Dot product = sum of products of corresponding components.
For nonzero vectors, angle = arccos[dot/(|a||b|)].
Cross product is shown only in three dimensions.
Frequently asked questions
Why is the cross product missing for other dimensions?
This tool uses the conventional three-dimensional cross product. Dot products, sums and differences work for the supported two to ten components.
Last updated . Results are estimates for informational purposes only.