Calculadora de Produto Vetorial — Formula

Cross Product

Formula

A × B = (a₂b₃ - a₃b₂, a₃b₁ - a₁b₃, a₁b₂ - a₂b₁)

Properties

  • The result is perpendicular to both input vectors
  • A × B=A×B × sin(theta) (area of parallelogram)
  • A × B = -(B × A) (anticommutative)
  • If A × B = (0,0,0), the vectors are parallel

    • Exemplo Resolvido

    Cross product of (2,3,4) and (5,6,7).

    1. x: 3×7 - 4×6 = 21 - 24 = -3
    2. y: 4×5 - 2×7 = 20 - 14 = 6
    3. z: 2×6 - 3×5 = 12 - 15 = -3
    4. A × B = (-3, 6, -3)
    5. |A × B| = √(9+36+9) = √54 ≈ 7.3485