calculating the surface area but with vector integral instead

[snow axle]

Objective: Integrate the surface area of any surface with Stoke's theorem.
To construct a vector field that has the same property when integrating, I defined F=<x,y,z>
However, curl F will be 0 if I defined that way, which will result in a surface area of 0, def not true.
Though it is redundant to do so, I'm just curious so please excuse. And please point out clearly if I have any problem, even with proof-writing or logical reasoning.

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@snow axle

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Hello denvau4618, this is a friendly reminder that your help request has been inactive for more than 24 hours. If you no longer need assistance, please consider closing the thread using the +close command. This thread will be automatically closed in 3 days if it remains inactive.

[snow axle]

+close

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