In 3D, a cross product takes two vectors and returns a vector. Geometrically, the magnitude of the result equals to parallelogram area and the direction is orthogonal to both vectors.
Properties
is orthogonal to both and - The vectors
, , are right handed (anti-commutativity) and (distributivity) (associativity)
Cross Product, Determinant, and Angle
We can have a precise definition of the cross product without the right hand rule by using determinant:
Formula:
Cross Product as Quarter Rotation
An observation for manipulating vectors in 3D:
cross product with a unit vector