The three-dimensional rectangular coordinate system consists of three perpendicular axes: the x-axis, the y-axis, the z-axis, and an origin at the point of intersection (0) of the axes. It represents the three dimensions we encounter in real life. We call this system the three-dimensional rectangular coordinate system. We can add a third dimension, the z-axis, which is perpendicular to both the x-axis and the y-axis.
Three-Dimensional Coordinate SystemsĪs we have learned, the two-dimensional rectangular coordinate system contains two perpendicular axes: the horizontal x-axis and the vertical y-axis.
This section presents a natural extension of the two-dimensional Cartesian coordinate plane into three dimensions. Does your planned route go through the mountains? Do you have to cross a river? To appreciate fully the impact of these geographic features, you must use three dimensions. For example, although a two-dimensional map is a useful tool for navigating from one place to another, in some cases the topography of the land is important. To expand the use of vectors to more realistic applications, it is necessary to create a framework for describing three-dimensional space. Life, however, happens in three dimensions. Vectors are useful tools for solving two-dimensional problems.
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