I'm making my way through proving many of the Vector differential identities. Even though it's hardcore math juggling on some of the larger ones, proving the whole thing is tedious work at best.
For any of these larger vector differential identities; for example nabla x (F x G) = (nabla * G)F.... . Is it generally accepted to prove only one of the components, say i, and say that the other two (j and k) will turn out the same? Is there any rule in calculus that says we can do that? If yes, could someone tell me the name of that rule?
Generally i'm always thinking in exam terms, so would this be acceptable as a proof during an exam.