Vectors

Abstract

Up to now we have used real numbers to represent the magnitude of physical quantities, such as mass and length, which are unrelated to any direction in space. We shall call such quantities scalars: they obey the ordinary rules of algebra. However, there are many physical quantities, such as velocity and force, which are only specified completely when a direction is given as well as a magnitude. We call such quantities vectors and we shall develop an algebra for their manipulation. In many applications we shall find that this leads to very elegant and concise solutions. When we have to apply the result to a practical situation, we usually find it necessary to describe the vectors in terms of their coordinates. For this reason, as well as to ease the derivation of algebraic rules for vectors, we start with a brief study of coordinate systems.