Elementary Concepts of Vector Algebra

So far we have only spoken of where an object is. To describe motion fully we need to talk about quantities that have both a size and, often, a direction — and that calls for a sharper vocabulary than plain numbers can give.

A scalar is a physical quantity completely specified by a magnitude (a number, with appropriate units) alone — it has no associated direction. Examples: distance, mass, temperature, speed, energy, time, density. Scalars combine by ordinary algebra: two masses of 3 kg and 5 kg simply add to 8 kg, with no need to worry about direction. …