Cross Product Calculator
Calculate the cross product of two 3D vectors and view the perpendicular result vector and its magnitude.
Enter two 3D vectors A = (x, y, z) and B = (x, y, z). The result is A × B.
Vector A
Vector B
Result will appear here.
| Metric | Value |
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Privacy: calculations run locally in your browser. No vector values are stored or transmitted.
How it works
For vectors A = (a₁, a₂, a₃) and B = (b₁, b₂, b₃),
the cross product is:
A × B = (a₂b₃ − a₃b₂, a₃b₁ − a₁b₃, a₁b₂ − a₂b₁)
Examples
- (1, 0, 0) × (0, 1, 0) = (0, 0, 1)
- (1, 2, 3) × (4, 5, 6) = (-3, 6, -3)
FAQ
- What is a cross product?
The cross product combines two 3D vectors and returns a new 3D vector perpendicular to both input vectors.
- Does cross product work in any dimension?
This calculator is for 3D vectors. The standard vector cross product is defined in 3D.
- What does a zero cross product mean?
A zero result means the vectors are parallel, anti-parallel, or one of them is the zero vector.
- Are calculations stored?
No. Everything runs locally in your browser.