Gibbs/Heavysides style vectors are convenient because it works with our 3D intuition, but Grassman/Clifford style works better for the differential calculus of gradient decent, hyper planes of DBScan, computer graphics etc...
Here is a programer friendly site that may be of help for those who are interested.
The geometric product being the sum of the exterior and dot products also solves a lot of things you run into with vector and tensor analysis.
I like to think of GA as strongly-typed matrix algebra. Instead of putting everything into one type (a matrix of numbers), it recognises and makes explicit physical concepts such as surfaces and volumes.
Gibbs/Heavysides style vectors are convenient because it works with our 3D intuition, but Grassman/Clifford style works better for the differential calculus of gradient decent, hyper planes of DBScan, computer graphics etc...
Here is a programer friendly site that may be of help for those who are interested.
The geometric product being the sum of the exterior and dot products also solves a lot of things you run into with vector and tensor analysis.
https://bivector.net/