Dividing by zero is not right, absolutely agree.
Maybe you should outline your basis and your two initial basis vectors that you want to use for orthonormalization purposes.
I'm supposed to use the Gram-Schmidt process to create Legrende polynomials. Usually when doing Gram-Schmidt, I first use it to create a set of orthogonal basises, then I divide every one of them by their norm to make the set orthonormal.
However, in this case, I suddently got to the point where I'm dividing a polynomial by zero, and that can't be right. I then tried to normalize each vector before proceeding to the next, and this time I didn't have the same problem, and I got the right answer in the end.
My question is basically, does this sometimes happen, that you can't create an orthogonal set of vectors first, or did I do something wrong with my calculations the first time?