The cross product A × B produces a vector perpendicular to both A and B. Its magnitude equals |A||B|sin(θ), giving the area of the parallelogram formed by A and B. Direction follows the right-hand rule. Unlike dot product, cross product is only defined in 3D and produces a vector, not a scalar.
How to Use
Enter two 3D vectors:
- Vector A: (a₁, a₂, a₃)
- Vector B: (b₁, b₂, b₃)
- Result: A × B vector computed
Formula
A × B = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁). Use the determinant method with i, j, k unit vectors.
Applications
- Torque: τ = r × F
- Magnetic force: F = qv × B
- Surface normals in 3D graphics
- Area of parallelogram/triangle
Step-by-Step Instructions
- 1Enter Vector A components.
- 2Enter Vector B components.
- 3View the cross product vector.
- 4Check its magnitude.
- 5Verify perpendicularity.