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3D Dot Product — result sheet
Calculate the scalar dot product of two three-dimensional Cartesian vectors from their six ordered components.
Inputs used
Results
Visual chart
Breakdown
Calculation steps
Returned data table
Formula and methodology
Formula: A dot B = ax bx + ay by + az bz.
The dot product multiplies corresponding components of two three-dimensional vectors and adds the three products. It returns one scalar that describes alignment in their shared Cartesian coordinate system.
This result follows the calculator's declared inputs, precision, validation boundaries, and model limits.
Input contract
- Vector A x — The x component of vector A.; minimum -1000000; maximum 1000000
- Vector A y — The y component of vector A.; minimum -1000000; maximum 1000000
- Vector A z — The z component of vector A.; minimum -1000000; maximum 1000000
- Vector B x — The x component of vector B.; minimum -1000000; maximum 1000000
- Vector B y — The y component of vector B.; minimum -1000000; maximum 1000000
- Vector B z — The z component of vector B.; minimum -1000000; maximum 1000000
Worked example
| Input | 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 |
A dot B = 1 x 4 + 2 x 5 + 3 x 6 = 32.
Assumptions and limits
- A and B are Cartesian 3D vectors whose components use the same coordinate basis and compatible units.
- The result is scalar arithmetic only; no angle, projection, physical force, or unit conversion is inferred.
Calculator note
Source and methodology
Use the official WorldCalculate methodology policy for the source, formula, precision, and boundary standards behind this calculator.
Planning estimate, not financial, medical, legal, or professional advice. © WorldCalculate — reuse with attribution. Built and curated by Hassan ALRowaie.
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