This appendix contains a brief outline of vector algebra and vector calculus. The essential purpose of vector algebra
is to convert the propositions of Euclidean geometry in three-dimensional
space into a convenient algebraic form. Vector calculus allows us to define
the instantaneous velocity and acceleration of a moving object in three-dimensional space, as
well as the work done when such an object travels along a general
curved trajectory in a force field. Vector calculus also introduces the concept of a scalar
field—for example, the potential energy associated with a conservative force field—and a vector field—for
example, an electric field.
