*sigh* I did all the work but it came out wrong :(
The normal vector of a plane ax+by+cz+d=0 is specified by [a b c], so the normal vector for 12x+y-3z = 0 is [12 1 -3].
The normal vector of a surface f(x,y,z) at point (x0,y0,z0) is [fx fy fz], so the normal vector for 2x2+y2-z2=64 is [4x0...