Vector Analysis

Not every physical quantity can be completely specified by a number and a unit alone. Consider a man who walks for a certain time at a certain speed: knowing only the time and the speed tells you the distance he has covered, but not where he has ended up — for that you also need to know the direction in which he walked.

This observation leads to a fundamental division of physical quantities into two classes. A scalar quantity is completely described by a magnitude (a number together with a unit) alone — examples include distance travelled, mass, time, temperature, and density. A vector quantity needs both a magnitude and a direction for its complete description — examples include displacement, velocity, force, and momentum. …