not to be confused with outer product. Note that the exterior product is sometimes called outer product in literatures.

The exterior product, also called wedge product, of vectors and constructs a bivector represents the parallelogram formed by the the vectors    and  , in the plane they span together. 1

exterior product is closely related to the cross product: exterior_product.jpg

Properties

  • Distributive over addition:

Magnitude

The magnitude of exterior product is the same as the magnitude cross product.

Theorem

Let be an orthonormal basis for a plane. Orient the plane with that of . Let and be vectors in the plane. Let be the oriented angle from to , . Then

In 3D

So far we are talking about the coordinate-free definition of exterior product, and here is a definition with three coordinate vectors:

Let and . Then

and

Footnotes

  1. Let’s remove Quaternions from every 3D Engine (An Interactive Introduction to Rotors from Geometric Algebra) - Marc ten Bosch