determine the normal to a plane using PCA

I have measured data that should represent a plane. I use princomp to remove tilt to the data in Z. I am interested in knowing the angle of tilt from Z to the normal of the original data. It seems like you should be able to use the coeffs calculated from princomp to get the normal vector which you can use to calculate the angle. Is this true? Alternatively, is there a way to calculate the normal vector of a data set?