Scalars and vectors

A scalar is fully described by a single number: mass, temperature, and energy are all scalars — "5 kg" is complete on its own. A vector needs a direction too: "5 N" isn't a complete description of a force until you also say which way it points.

This distinction isn't just bookkeeping. Two forces of equal size pointing in opposite directions add up to zero, while two forces of equal size pointing the same way add up to double — the direction changes the answer completely, which is exactly why vectors can never be added the way plain numbers are.

A quick way to spot a vector: ask whether "which direction?" is a sensible follow-up question. It makes sense for force, velocity, and displacement. It doesn't make sense for mass, time, or energy — there's no such thing as "3 kg pointing north."