Result
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Formula and methodology
For 3D vectors, A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁). The 2D mode returns aₓbᵧ − aᵧbₓ, the scalar z-component after embedding both vectors in the xy-plane.
Worked example
For A = (1, 2, 3) and B = (4, 5, 6), A × B = (−3, 6, −3) and its magnitude is √54 ≈ 7.348469.
Assumptions and boundaries
- Cross-product order matters: B × A is the negative of A × B.
- Parallel vectors have the zero vector as their cross product.
- The 2D result is a scalar z-component, not a two-component cross-product vector.
- This page does not calculate a standalone dot product.
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