How to Calculate Vector Cross Product
Calculate A × B for two 3D vectors, then see the parallelogram area, triangle area, and unit normal direction.
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Calculate the cross product
How to calculate a vector cross product
A × B = ⟨a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁⟩
The output is perpendicular to both inputs and its direction follows the right-hand rule. Reversing the order changes the sign: B × A = −(A × B).
Geometric meaning
|A × B| is the area of the parallelogram spanned by A and B; half is the corresponding triangle area. Parallel vectors produce the zero vector and no unique unit normal. See OpenStax's cross-product reference.