In science, mathematics, and engineering, we distinguish two important quantities: scalars and vectors. A scalar is simply a real number or a quantity that has magnitude. For example, length, temperature, and blood pressure are represented by numbers such as 80 m, 20°C, and the systolic/diastolic ratio 120/80, respectively. A vector, on the other hand, is usually described as a quantity that has both magnitude and direction.
Geometrically, a vector can be represented by a directed line segment—that is, by an arrow—and is denoted either by a boldface symbol or by a symbol with an arrow over ...