Certified calculator · Version 1

Vector Calculator

Compare two three-dimensional vectors using deterministic Euclidean vector operations.

AₓAᵧA_zBₓBᵧB_z

Dot product0

Cross product(0, 0, 1)

|A|1

|B|1

Angle (radians)1.57

CalcuMint Pro

Advanced Analysis

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Advanced chartsExplore the result across time and assumptions.

Scenario comparisonCompare multiple assumptions side by side.

Sensitivity analysisSee which assumptions change the outcome most.

Goal SolverSolve backwards from the outcome you want.

Result methodology

The certified vector engine computes dot product, cross product and magnitudes from the same validated components, then derives the included angle when defined.

Solution steps

A·B = 0
|A| = 1, |B| = 1
A×B = (0, 0, 1)

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.

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.