(Click here to display equations 37, 39, 40 and 50, which are discussed below)

Fit a plane to the points (1,1,1), (0,2,1) and (2,2,-1). Using Equation 39

The determinant is from Equation 40. Hence the equation of the plane is 3-x-y-z=0 or x+y+z=3.

Alternatively, using Equations 37 and 50

and the determinant of is 4. Then compute

So the planar coefficients are c=3, a=-1 and b=-1. Hence , or , as before.