Chapter 1: the coordinate systems

The coordinate systems
From a mathematical point of view it is very convenient to work with vectors when they are resolved into components along three mutually orthogonal (perpendicular) directions. In this lecture, we will mainly use three orthogonal coordinate systems: the rectangular (or Cartesian) coordinate system, the cylindrical (circular) coordinate system, and the spherical coordinate system. We shall now digress to discuss each of these coordinate systems and then resume our discussion of vectors.

Rectangular coordinate system
A rectangular (Cartesian) coordinate system is a system formed by three
mutually orthogonal straight lines. The three straight lines are called the
x, y, and z axes. The point of intersection of these axes is the origin.

We will use the unit vectors ax, ay and az to indicate the directions of
the components of a vector along the x, y, and z axes, respectively.