Calculadora de Produto Vetorial
Calcule o produto vetorial de dois vetores 3D.
Cx
-3.0000
Magnitude7.3485
Formula
Cross Product
Formula
A × B = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁)
Properties
Exemplo Resolvido
Cross product of (2,3,4) and (5,6,7).
- 01x: 3×7 - 4×6 = 21 - 24 = -3
- 02y: 4×5 - 2×7 = 20 - 14 = 6
- 03z: 2×6 - 3×5 = 12 - 15 = -3
- 04A × B = (-3, 6, -3)
- 05|A × B| = √(9+36+9) = √54 ≈ 7.3485
Perguntas Frequentes
What is the cross product?
The cross product of two 3D vectors produces a vector perpendicular to both inputs. Its magnitude equals the area of the parallelogram formed by the two vectors.
Does the cross product work in 2D?
The cross product is only defined for 3D vectors. In 2D, you can treat vectors as 3D with z=0, and the result will point entirely in the z direction.
What does the magnitude represent?
The magnitude of A × B equals |A|×|B|×sin(theta), which is the area of the parallelogram spanned by the two vectors.
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