For this post, I decided to ask what I think is a very simple question. It is simple at first, but it also gets to the heart of the meaning of vector quantities, at least as they are typically presented in introductory physics. It also emphasizes the fact that vector quantities have an existence all their own, independent of our arbitrary coordinate systems.
A particle moves through space with momentum 5 SI units. Resolve the particle’s momentum vector into components in each of the following ways: (a) the momentum vector has one nonzero component (b) the momentum vector has two nonzero components (c) the momentum vector has three nonzero components.
Be aware that there are infinitely many “correct” responses to this question. If you don’t like momentum, you can use any other vector quantity. Go!