#########################################################################
# Returns the normal equation of the plane through 3 points a,b,c in 3D.
# Usage:  P3points(<1,0,0>, <1,1,0>, <0,1,1>);
# returns  -x - z + 1 = 0.
#########################################################################
P3points := proc (a, b, c) 
 local ex1, ex2, n, r; 
 global x, y, z; 
 r := <x,y,z>; 
 n := LinearAlgebra:-CrossProduct(b-a,c-a); 
 ex1 := `assuming`(LinearAlgebra:-DotProduct(n,r-a),real); 
 ex2 := collect(ex1,[x, y, z]); 
 ex2 := sort(ex2,[x, y, z]); 
 RETURN(ex2 = 0) 
end proc;