Some physical quantities, such as time, mass, and temperature, can be described completely by a single number with a unit. For example, the mass of an object is 6 kg and its temperature is . A single number (with a unit) that describes a physical quantity is called a scalar. A scalar can be positive, negative, or zero.
Many other quantities, however, have a directional aspect and cannot be described by a single number. To describe the motion of a car, for example, you must specify not only how fast it is moving, but also the direction in which it is moving. A quantity having both a size (the “How far?” or “How fast?”) and a direction (the “Which way?”) is called a vector. The size or length of a vector is called its magnitude. Vectors will be studied thoroughly in Chapter 3, so all we need for now is a little basic information.
We indicate a vector by drawing an arrow over the letter that represents the quantity. Thus and are symbols for vectors, whereas r and A, without the arrows, are symbols for scalars. In handwritten work you must draw arrows over all symbols that represent vectors. This may seem strange until you get used to it, but it is very important because we will often use both r and , or both A and , in the same problem, and they mean different things! Note that the arrow over the symbol always points to the right, regardless of which direction the actual vector points. Thus we write or , never or .