Find the cross product of two 3D vectors — a vector perpendicular to both. Enter both as three components.
Usage Tip
If the cross product is the zero vector, the two vectors are parallel.
Perpendicular to both inputs
Its length equals the area of the parallelogram they form.
The result is perpendicular to both inputs.
Its magnitude is the area of the parallelogram spanned by the vectors.
The cross product of two vectors in three dimensions produces a new vector that is perpendicular to both of them. Its length equals the area of the parallelogram the two vectors span, which is the product of their lengths times the sine of the angle between them. The direction follows the right hand rule.
Order matters: swapping the two vectors reverses the direction of the result, so A cross B equals minus B cross A. The cross product is zero when the vectors are parallel. It is used to find surface normals, torque from a force and a lever arm, and the area of a triangle, which is half the length of the cross product of two of its edges.