Find equations of the normal line?

Question

Find equations of the normal line to z=sinx cosy at (0, pi, 0).

Answer: x=-t, y=pi, z=-t.

Fx=cosx cosy

Fy=-sinx siny

 

Answer 1

F(x,y,z) = sinx cosy - z = 0

Fx = cosx cosy = -1 at (0, pi, 0)

Fy = -sinx siny = 0 at (0, pi, 0)

Fz = 1 at (0, pi, 0)

So, the normal line is

(x-0)/(-1) = (z-0)/(1) = t, and y = constant = pi, since Fy = 0, there is no change in y-direction

Or,

x = -t

y = pi

z = -t