Cross Product Calculator
Calculate the cross product of two 3D vectors.
Formula
A × B = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁)
- A × B = (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁)
Cross Product of Two Vectors
Inputs
- a₁: 1
- a₂: 2
- a₃: 3
- b₁: 4
- b₂: 5
- b₃: 6
Suppose A = (1, 2, 3) and B = (4, 5, 6). The cross product A × B = (12-15, 18-4, 5-8) = (-3, 14, -3) with magnitude √(9+196+9) ≈ 14.36.
Frequently asked questions
What is the cross product?
The cross product A × B of two 3D vectors results in a vector perpendicular to both. Formula: (a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁).
What does the magnitude represent?
The magnitude |A × B| equals the area of the parallelogram formed by A and B.
When is the cross product zero?
When vectors are parallel or either is zero.
What is the right-hand rule?
Point fingers along A, curl toward B; thumb points in direction of A × B.