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u × v yields the vector perpendicular to both inputs (right-hand rule), with magnitude |u||v|sin θ. Reference: i × j = k, j × k = i, k × i = j.
3D perpendicular vector with the basis-vector reference.
u × v = (u₂v₃−u₃v₂, u₃v₁−u₁v₃, u₁v₂−u₂v₁)
| Symbol | Meaning |
|---|---|
| u × v | Perpendicular (axial) vector |
(1,0,0) × (0,1,0) = (0,0,1) — i.e. i × j = k. (2,3,4)×(5,6,7) = (−3,6,−3).
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The cross product is defined in 3D (and 7D); 2D vectors have no unique perpendicular vector.
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Content updated: September 2026