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1. The problem statement, all variables and given/known data

Is the gradient perpendicular to all surfaces or just level surfaces?

For instance, if I I have a function f(x,y)=z where z is the dependent variable then that is a surface, wouldn't that be a level surface to a function of x,y,z so shouldn't the gradient also be perpendicular to the surface and level surface?

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# B Gradient and direction

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