Technical Mathematics, Sixth Edition

7.5. Introduction to Vectors

7.5.1. Vector and Scalar Quantities

Many quantities in technology cannot be described fully without giving their direction as well as their magnitude. It is not always useful to know how fast something is moving, for example, without knowing the direction in which it is moving. Velocity is called a vector quantity, having both magnitude and direction, as opposed to, say, weight, which is called a scalar quantity. The weight of a football is a scalar quantity, but its velocity at any instant is a vector quantity. Other vector quantities include force and acceleration; other scalar quantities include time and volume.

7.5.2. Representation of a Vector

A vector is represented by an arrow whose length is proportional to the magnitude of the vector and whose direction is the same as the direction of the vector quantity (Fig. 7-39).

Figure 7.39. Representation of a vector.

Vectors are represented differently in different textbooks, but they are usually written in boldface type. Here, we'll use the most common notation: boldface Roman capitals to represent vectors, and nonboldface italic capitals to represent scalar quantities. So in this textbook, B is understood to be a vector quantity, having both magnitude and direction, while B is understood to be a scalar quantity, having magnitude but no direction. Boldface letters, however, are not practical in ...