Most of the last sections (all intersections) feel like corner cases, when in PGA they are one and the same.
You get transformations too, as easy as M=b/a, where M can be applied to any element in the algebra by taking the square root and applying double-sided multiplication such that b = √M a ~√M, where tilde represents the reverse. These transformations are isomorphic to complex numbers, quaternions, and hypercomplex numbers, and understanding them makes other explanations of these concepts feel inadequate and woefully un-geometric.
Add in logarithms and the exponential map for these transformations and we can perform linear interpolation between states and parametrize transformations.
I'm just a motivated amateur and I can do all of these things. The vector algebra I learned in engineering is useful, and it's often all I need for simple 3-dimensional problems, but it's just shy of something far more powerful and far more general.
Edit: nevermind, read in other comments that https://bivector.net/ has a ton of resources.
https://github.com/jeremyong/klein
I've always wanted to find an excuse to rebuild some projects at work around this.