Three-Dimensional Coordinate Systems
Jim LambersMAT 169Fall Semester 2009-10Lecture 17 NotesThese notes correspond to Section in the Coordinate SystemsOver the course of the next several lectures, we will learn how to work with locations and directionsin Three-Dimensional space, in order to easily describe objects such as lines, planes and curves. Thiswill set the stage for the study of functions of two variables, the graphs of which are surfaces in Three-Dimensional SpacePreviously, we have identified a point in the -plane by an ordered pair that consists of two realnumbers, an - Coordinate and - Coordinate , which denote signed distances along the -axis and -axis, respectively, from the origin, which is the point (0,0). These axes, which are collectivelyreferred to as the Coordinate axes, divided the plane into four now generalize these concepts to Three-Dimensional space, or -space. In this space, apoint is represented by anordered triple( , , ) that consists of three numbers, an -coordiante, a - Coordinate , and a - Coordinate .
Figure 1: The point (2;3;1) in xyz-space, denoted by the letter P. The origin is denoted by the letter O. The projections of P onto the coordinate planes are indicated by the diamonds.
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