Cross product
where is perpendicular to both vectors and is right-handed.
Properties
For and :
- iff for some , or either vector is zero
Geometric interpretations
is the area of the parallelogram formed by and , so the triangle with , has area . Fixing and restricting to , the map scales by and rotates it by within the plane orthogonal to .
Component expression
With cyclically, for and :
Equivalently, this is the formal determinant
Related
Stated in
- Definition 2.18 (Vector Product In )§2.4 Vector Product (Cross Product) in