What is the point in calculating orthonormal bases for R3

Main Question or Discussion Point

I'm just learning linear algebra, where we are taking a set of basis vectors and then using gram schmidt to convert them to an orthonormal basis.

So I know I can do it. I know orthonormal is great. But as I'm modifying the basis anyway from the original, why don't I just forget the original basis and just use (0,0,1) (1,0,0) (0,1,0) and be done with it.

Is some useful information being preserved from the original basis into the orthonormal basis? I'm looking for some motivation for this process.

Thanks,

Sean

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