This page became really too long and so I decided to create a PDF booklet about the subject. Good news: you can just download and read it.
This reference and textbook on vectors and coordinates focuses on mathematics and programming solutions. As an easy-to-read work, it forms a practical collection on CAD faces, vectors, angles, normals, projections, rotations and more. Code fragments are written in CAD Lisp and therefore usable in programmes such as BricsCAD and AutoCAD.
You can find it here: https://nedcad.nl/coordinate-mathematics-for-cad/