Earlier quoted context omitted.
As a physicist myself, I find I think of vectors more often as a set of independent magnitudes for each of the coordinate system axes, than of a single magnitude with a direction. That's because in most cases, the physics just works independently in each axis. So it makes a lot of sense to treat vectors as sets of numbers. Most calculations physicists do are the same as pure mathematicians would do. So we use for exa…
> I find I think of vectors more often as a set of independent magnitudes for each of the coordinate system axes Interesting. This is what Hestenes calls the “coordinate virus”, http://geocalc.clas.asu.edu/pdf/MathViruses.pdf ; very often any specific coordinate system is not inherent but is some arbitrary addition to the space made for convenience in some particular calculation. It is in my opinion a mistake to thin…
Not really. I didn't say in the first statement that a specific coordinate system was used. In most systems, it doesn't matter how you choose your coordinate system, as long as the basis is orthogonal, treating the coordinates independently of each other will work.