Conference rusure::math

    Take the direction of the cross product of vectors from one point
    to each of the other two points:
    
    	| x2-x1 x3-x1 i |
    	| y2-y1 y3-y1 j |
    	| z2-z1 z3-z1 k |
    
    That gives you the direction of a line normal to the plane.
    
    
    				-- edp

This is as good a place to ask as any...

My solid geometry is terrible, as is my linear algebra, but I think
that the dot product of the normal vector with any vector in the plane
should be 0, so you can solve the set of equations:

(x1-x2)x + (y1-y2)y + (z1-z2)z = 0

(x1-x3)x + (y1-y3)y + (z1-z3)z = 0

(x2-x3)x + (y2-y3)y + (z2-z3)z = 0

	 2    2    2
and	x  + y  + z  = 1

for x, y and z; (x,y,z) is a unit vector normal to the plane. If the system
of equations doesn't have a unique solution then two or more of your points
are collinear.
							Richie

    Re .2,

    Solving those equations, you encounter a matrix of cofactors, which
    happen to be the cross product in 3 dimensions.

    - Jim

< Note 626.0 by MMO03::DANTONI "Gaitan D'Antoni" >
                         -< Normal to a plane in 3d? >-

    I'm not sure if this is where to ask this but here goes...
    
    Given three points in space (x1,y1,z1), (x2,y2,z2), and (x3,y3,z3), and
    a plane, P, defined by these three points, what is the formula for
    finding the normal, N, to the plane P?
    
    Gaitan

>	Since any two points in the plane define a line in the plane,
>	and any line normal to that plane must be parallel to the
>	vector cross product of any pair of distinct vectors in that
>	plane, one normal vector would be:

>	N1 = ( x1, y1, z1 ) cross ( x2, y2, z2 )

>	   = ( y1*z2 - y2*z1,
>	       x2*z1 - x1*z2,
>	       x1*y2 - x2*y1 )  

>	The line passing through point ( x0, y0, z0 ) and parallel
>	to the non-zero vector ( a, b, c ) has the parametric
>	equations:

>	x = x0 + a*t, y = y0 + b*t, z = z0 + c*t

>	Use N1.x, N1.y, and N1.z for a, b, c respectively.
>	A family of lines is thus defined corresponding to different
>	values of x0, y0, and z0.