When you are defining a coordinate system when solving a problem, do the coordinates need to be right-handed to obtain a correct solution? I feel like the answer is no because the directions of vectors like torque should be independent of the coordinate system we choose; they will just be represented by different coordinates. Therefore, I think that a left-handed coordinate system (if chosen for convenience) would still yield correct answers. Is my thinking correct?
Does it ever become important to stick to a right-handed coordinate system in higher-level physics?