Actually, had a better idea: the contour is f(x,y,z)=0 so the tangent plane to the countour isI am not sure what to do, but I was thinking may be try to express z as the function of x and y and apply the same template as in (ii)
so that I get and as per the answer in the book.
Now I need to figure out the way to find the normal vector. BUT it's probably the coefficients of x, y and z in the above equation, right? So, the normal vector is .
Any comments are still welcome!