How this calculator works
The engine evaluates A·B, A×B and each magnitude, then derives the included angle from the normalized dot product when both vectors are non-zero.
Formula
A·B; A×B; |A|; θ=acos((A·B)/(|A||B|))Computes common deterministic 3D vector operations.
Worked example
Unit axes is a verified test case used by the calculation engine.
Assumptions and limitations
- Vectors use three real components.
- The angle is undefined when either vector has zero magnitude.
Methodology & sources
This calculator uses deterministic, versioned calculation logic. The formula and verified examples above are part of the calculation definition used by CalcuMint. Technical calculation version: 1.
- CalcuMint deterministic vector engine — Standard Euclidean vector identities.
Frequently asked questions
Does it calculate a cross product?
Yes. The full 3D cross-product vector is returned.
What angle unit is used?
The deterministic engine reports the angle in radians.