Planes in Space

The simplest planes are those where two of the numbers a, b, c are zero.

The plane x = d is parallel to the yz-plane. The plane y = d is parallel to the xz-plane. The plane z = d is parallel to the xy-plane.

These three cases are illustrated in Figure 10.5.1.

Figure 10.5.1

The examples below show how to draw sketches to help visualize other planes. The idea is to use the points where the plane cuts the coordinate axes, and to draw a triangular or rectangular portion of the plane.

Example 1: For sketching a plane where a, b, c and d are nonzero.

Example 2: Sketching a Plane Where Two of a, b, c Are Nonzero and d ≠ 0.)

Example 3: Sketching a Plane with d = 0