A Swift Introduction to Geometric Algebra

You're in for a nice trip, the concept is called Geometric Algebra: ▶ this video (~50m video) TLDW: Yes, the concept is there, makes much more sense than a cross product (which is just an oriented area) and generalizes really nicely. Alternatively, read: link

Note don't to be confused with Algebraic Geometry they are different; When I first came across this topic it was eye opening, especially the fact that you could squeeze Maxwell's equations into one and the fact that pseudovector create by cross product from physics is just a bivector which in 3d could be represented like a vector orthogonal to the plane created by the two vectors in the product Primer on the topic ▶ this video (And other videos on his channel) Another greate playlist is link BTW the author has the following page link with great infographics and references

You should jump straight to geometric algebra. It's actually simple there. Quaternions and Complex Numbers are about just some not so special multivectors. Here are 2 45mn videos you'll not regret: link ▶ this video

Also check out ▶ this video and link Some of the perceived complexity of complex numbers and quaternions seems to stem from not knowing the bigger picture.

If you want an inspiring (imho) overview of the power of geometric algebra, I thoroughly enjoyed the video "A Swift Introduction to Geometric Algebra" ▶ this video

This little known channel: sudgylacmoe - which doesn't seem present in the list, has the best video by far on Geometric Algebra (imho) ▶ this video

I highly recommend the video ▶ this video linked from the site above ~40 minutes, and I get the point of geometric algebra now.