I don't understand what you mean by "f is constant". If y= f(x)= C, the graph is a horizontal line in the xy-plane and vectors normal to it are of the form <0, a> for any number, a. If z= f(x,y)= C, the graph is a plane parallel to the xy-plane and vectors normal to it are of the form <0, 0, a> for any number, a.

vectorsdo not form a linearly ordered set. It makes no sense to talk about maximum or minimum vectors. Youcantalk about maximum or minimum length of a set of vectors. is that what you meant?