If you have a function, f, in cylindrical coordinates, can you normalize the function (in a rigorous sense)?
\[f(r,\phi,z)=a*r^{"^"}+b*\phi ^{"^"}+c*z^{"^"}\]
You can find the magnitude by
\[\sqrt{a^2+c^2}\]
but can you truly normalize the function and apply that to a mathematical formula which requires the normalized vector. Or do you have to transform back to rectangular coordinates before normalizing? I have looked through several textbooks and the internet and cannot find anything about normalizing a vector in the cylindrical system.

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