Trying to understand a concept on vector calculus, the book states:(adsbygoogle = window.adsbygoogle || []).push({});

If S is a surface represented by

[tex]\textbf{r}(u,v) = u\textbf{i} + v\textbf{j} + f(u,v)\textbf{k}[/tex]

Any curver(λ), where λ is a parameter, on the surface S can be represented by a pair of equations relating the parameters u and v, for example u = f(λ) and v = g(λ).

What exactly is the justification or proof for this statement?

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# Equation of a curve on a surface

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