DIMENSIONAL GEOMETRY

INTRODUCTION TO THREE DIMENSIONAL GEOMETRY . Coordinate Axes and Coordinate Planes in Three Dimensional Space Consider three planes intersecting at a point O such that these three planes are mutually perpendicular to each other (Fig . ). These three planes intersect along the lines X ′ OX, Y ′ OY and Z ′ OZ, called the x , y and z - axes , respectively.

We may note that these lines are mutually perpendicular to each other. These lines constitute the rectangular coordinate system . The planes XOY, YOZ and ZOX, called, respectively the XY- plane , YZ- plane and the ZX- plane , are known as the three coordinate planes. We take the XOY plane as the plane of the paper and the line Z ′ OZ as perpendicular to the plane XOY.

If the plane of the paper is considered as horizontal, then the line Z ′ OZ will be vertical. The distances measured from XY-plane upwards in the direction of OZ are taken as positive and those measured downwards in the direction of OZ ′ are taken as negative. Similarly, the distance measured to the right of ZX-plane along OY are taken as positive, to the left of ZX-plane and along OY ′ as negative, in front of the YZ-plane along OX as positive and to the back of it along OX ′ as negative. The point O is called the origin of the coordinate system.

The three coordinate planes divide the space into eight parts known as octants . These octants could be named as XOYZ, X ′ OYZ, X ′ OY ′ Z, XOY ′ Z, XOYZ ′ , X ′ OYZ ′ , X ′ OY ′ Z ′ and XOY ′ Z ′ . and denoted by I, II, III, ..., VIII , respectively.