Engineering Mathematics

11

Three-Dimensional Geometry

11.1 COORDINATE PLANES

Consider the right-handed three-dimensional coordinate system with origin O. The planes passing through the axes, taken two at a time, define the coordinate planes. Thus, the plane XOY passing through the axes OX and OY defines xy-plane, the plane YOZ passing through the axes OY and OZ defines yz-plane, and the plane ZOX passing through the axes OZ and OX defines zx-plane.

Since the axes OX, OY, and OZ are mutually perpendicular, the coordinate planes are also mutually perpendicular. Let P(x, y, z) be any point in the space. Draw the perpendicular PM from P to the xy-plane. Then, by definition, PM = z. From M, draw perpendiculars MA and MB to the axes OX and OY, respectively, meeting the axes ...