i have a quick question regarding the unit normal vector on the following integral:
∫∫F•dS = ∫∫F•ndS
s s
if the surface S is given by z=g(x,y) then the unit normal vector is f(x,y,z)= z - g(x,y) ⇒
gradf(x,y,z)
n= -----------------
|gradf(x,y,z)|
my question is if i'm given the surface 3z=g(x,y), then what should the unit normal vector be???
is it f(x,y,z) = 3z - g(x,y) or f(x,y,z) = z - g(x,y)/3