Enter vectors A and B, then click Calculate Cross Product.

The cross product (also called the vector product) of two vectors in three-dimensional space produces a third vector that is perpendicular to both original vectors. For vectors a = (a₁, a₂, a₃) and b = (b₁, b₂, b₃), the cross product is defined as: a × b = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁). The magnitude of the cross product equals the area of the parallelogram formed by the two vectors, and equals |a||b|·sin(θ), where θ is the angle between them. The direction is given by the right-hand rule. The cross product is fundamental in physics (torque, angular momentum, magnetic force), engineering, computer graphics (normal vectors), and geometry. This calculator computes the cross product, its magnitude, the angle between vectors, and related geometric properties.

1. Enter the x, y, z components of Vector A.
2. Enter the x, y, z components of Vector B.
3. Click Calculate Cross Product to compute A × B.
4. The result shows the cross product vector, magnitude, angle, and area.
5. For perpendicular vectors, the cross product magnitude is maximal.
6. Click Reset to restore default example values.