I've learned to represent curl, rot and Laplacian in the general form using scaling factors, Levi Civita symbol and delta. I was asked to prove some general identities in vector calculus.
I was wondering, is it necessary to prove those identities under the general form (keeping the scaling factors in the statements)? Or can I prove the identities just for Cartesian coordinates, which has scaling factor h=1?
In every online source including Wikipedia, Wolfram and others, they use the tensor notation, neglecting the scaling factors. Is that ok to add the scaling factors only when solving the physical equations?