# Math Help - Normal Line and Tangent Plane

1. ## Normal Line and Tangent Plane

Hi, ive been trying to attempt this question but do not quite understand how to solve the problem. Is it possible for any1 to solve this so I can look through and get a better understanding. Thanks.

1) Find the normal line and tangent plane to the surface z = x^2 + y^2 + 2
at the point (1,1,4). At what point does the normal line meet the surface again?

2. ## Re: Normal Line and Tangent Plane

Originally Posted by NFS1
1) Find the normal line and tangent plane to the surface z = x^2 + y^2 + 2 at the point (1,1,4). At what point does the normal line meet the surface again?
The surface is $S(x,y,z)=x^2+y^2-z+2$.
The normal $\nabla S(x,y,z)=2x{\bf{i}}+2y{\bf{j}}-{\bf{k}}$.

Now $\nabla S(1,1,4)$ is the direction of the normal line and the normal of the tangent plane at $(1,1,4)$.