Yes,ifyou do it in that order- that is, normalize to unit length, then "Gram-Schmidt" , etc. Since the first three are already orthonormal, you would just get , , again. And since is a linear combination of them, it has no "part" that is perpendicular to the space spanned by them- Gram-Schmidt would give the 0 vector.

But if you started by normalizing , then projecting, say, onto that to find a vector perpendicular to you would get 3 completely different vectors.