In this video, we set up the geometric algebra of three dimensions, called G(3). We will see that the introduction of a third basis vector adds two extra bivectors and a trivector to our basis for G(3) compared to G(2). We’ll see that geometric interpretations and computations are analogous to G(2) and the new mathematical object, the trivector, is to be interpreted as a directed volume element, also called the pseudoscalar in G(3).
References / Further Reading:
1. Lasenby and Doran’s “Geometric Algebra for Physicists”.
2. Recommended video on Clifford algebra:
3. And other video series covering Geometric Algebra (Nick Okamoto): https://www.youtube.com/watch?v=P-IKemH3jsg&list=PLQ6JJNfj9jD_H3kUopCXkvvGoZqzYOzsV