14

Three-Dimensional Geometry

14.1 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 ...

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