TABLE OF CONTENTS A scalar physical quantity is described by a numerical factor with units. In general, the numerical factor will depend on the system of units we choose. Examples of scalars include mass, temperature, and time. Two scalars may be added or subtracted provided they have the same units. For example, it would be meaningless to add scalars of differing units such as temperature and time. Scalars of differing units may be multiplied or divided to form a new scalar, however, such as the average density obtained as the ratio of an object's mass to its volume.
A vector physical quantity is described by a numerical factor with units and a specified direction. Examples of vectors include electric and magnetic fields and forces that have a specified direction in space. Vectors are usually designated with boldfaced symbols such as A in printed work or with an arrow 
in handwritten work, such as on a chalkboard or on notebook paper.
A three-dimensional vector A may be expressed in Cartesian coordinates as
| (1.1) |  |
where i, j, and k are unit vectors in the x-, y-, and z-directions, respectively. A x, A y, and A z are the components of A along each coordinate axis. Given the vector B = B x i + B y j + B z k, the vector sum or difference A B may be written...
