What Are the Methods to Determine Surface Normal Direction at a Point?

[physiker99]

How do I find "surface normal direction" for a plane on a point with coordinates specified?

 

[ponjavic]

Do you have a plane equation or do you only have the coordinates of a point? Please be more specific.

 

[physiker99]

i need to find normal directions for r^2=9 and x+y+z^2=1 at the point (2,-2,1)

 

[gabbagabbahey]

i need to find normal directions for r^2=9 and x+y+z^2=1 at the point (2,-2,1)

First, neither of those surfaces are planes. The first is a spherical shell, and the second is a paraboloid.

Second, straight from wikipedia:

If[/PLAIN] a surface S is given implicitly as the set of points $(x,y,z)$ satisfying $F(x,y,z)=0$, then, a normal at a point $(x,y,z)$ on the surface is given by the gradient:

$$\mathbf{N}=\mathbf{\nabla}F$$

since the gradient at any point is perpendicular to the level set, and $F(x,y,z) = 0$ (the surface) is a level set of $F$.

I'd be shocked if this wasn't in your notes or textbook, and I strongly suggest you review the section of your text that covers this.

Anyways, just like wikipedia implies, to find a surface normal at a point, define $F$, take the gradient (in the appropriate coordinate system) and plug in the point.