How to Calculate Vector Cross Product
What is Vector Cross Product?
The cross product A×B of two 3D vectors produces a new vector perpendicular to both. Its magnitude equals the area of the parallelogram spanned by the two vectors. Direction follows the right-hand rule.
Step-by-Step Guide
- 1A×B = [a₂b₃−a₃b₂, a₃b₁−a₁b₃, a₁b₂−a₂b₁]
- 2Magnitude: |A×B| = |A||B|sin(θ)
- 3A×B = −(B×A) (anti-commutative)
Worked Examples
Input
A=[1,0,0] · B=[0,1,0]
Result
A×B = [0,0,1] (unit z-vector)
x̂ × ŷ = ẑ by right-hand rule
Ready to calculate? Try the free Vector Cross Product Calculator
Try it yourself →