Quote by garrett
Answering your other questions:
For now, [itex]r = \sqrt{x1^2 + x2^2 + x3^2}[/itex] is best thought of as just a notational convenience.

Ok, but there are surely some bounds on the validity of group element then as we expanded in a power series the answer is only going to be valid for small x and small r; the series will break down for large coordinates.