After having set up G(3), let's now investigate a particular geometric product, namely, the product between vector and bivector. We'll see that such a product in general splits into a vector part and the trivector part. Similar to the geometric product between vectors, we'll call the lower-graded vector part the dot product between vector and bivector and we'll call the higher-graded trivector part the wedge product. In this video, we'll motivate these definitions and save the algebraic exploration and geometric meaning for the second part.
References / Further Reading:
1. Lasenby and Doran's "Geometric Algebra for Physicists".
2. Recommended video on Clifford algebra:
https://www.youtube.com/watch?v=rqadK8-dN-Y
3. And other video series covering Geometric Algebra (Nick Okamoto): https://www.youtube.com/watch?v=P-IKemH3jsg&list=PLQ6JJNfj9jD_H3kUopCXkvvGoZqzYOzsV