>>10885421mutually perpendicular = orthogonal, which i assume you just looked at based on the text.
remember finding total force on a point in a 2D free body diagram?
no matter what direction the various arrows were pointing, you could always project them onto the x and y axes
this is what they're doing here only using three planes instead of 2 axes
as for the matrix ill leave that to some other anon, but it looks familiar from vector calculus or linalg, sorry i'm a brainlet and i brain dump anything i don't use on the regular
