Vectors

Abstract

When describing the behavior of a physical system, we specify certain physical quantities at various points in space and time. For example, a particle of a given mass may be described by its position and velocity at each space-time point. The behavior of air in a room can depend on thetemperature at each point in the room. Some of these quantities—mass, temperature, density—are completely specified by a single number with the appropriate units i.e., by a magnitude only. Such a physical quantity is called a scalar and is represented by a mathematical function of space and time called a scalar point function. We shall use italic type for symbols representing scalars (e.g., T for temperature). Others of these quantities (e.g., velocity, acceleration, force) require not only a magnitude but also a direction in order to be completely specified. For example, to specify the velocity of a particle, we must not only tell how fast the particle is moving (magnitude) but also tell in what direction it is traveling. A physical quantity of this kind is called a vector and is represented by a mathematical function of space and time called a vector point function. To denote a vector, we shall use boldface roman type (e.g., F for force).