After finding an orthogonal basis for a given set of vectors, I know it's okay to multiply any of the orthogonal vectors by a scalar, because this just changes the length of the vector and not it's direction (and hence not it's angle between any of the other vectors in the set).

However, is it okay to do this for any of the vectors in the equations used to find each orthognal vector in the first place? For example, the equation for finding the third orthogonal vector has vectors in it. Could I multiply any of these vectors by a scalar (to simplify calculations) and still get the correct answer?

Thanks!