A Note The coordinates of the origin O are ( , , ). The coordinates of any point on the x -axis will be as ( x , , ) and the coordinates of any point in the YZ-plane will be as ( , y , z ). Remark The sign of the coordinates of a point determine the octant in which the point lies. The following table shows the signs of the coordinates in eight octants.
Table . Fig . I II III IV V VI VII VIII – – – – – – – – z – – – – Octants Coordinates INTRODUCTION TO THREE DIMENSIONAL GEOMETRY Example In Fig . , if P is ( , , ), find the coordinates of F.
Solution For the point F, the distance measured along OY is zero. Therefore, the coordinates of F are ( , , ). Example Find the octant in which the points (– , , ) and (– , ,– ) lie. Solution From the Table .
, the point (– , , ) lies in second octant and the point (– , , – ) lies in octant VI. EXERCISE . . A point is on the x -axis.
What are its y -coordinate and z -coordinates? . A point is in the XZ-plane. What can you say about its y -coordinate?
. Name the octants in which the following points lie: ( , , ), ( , – , ), ( , – , – ), ( , , – ), (– , , – ), (– , , ), (– , – , ) (– , – , – ). . Fill in the blanks: The x -axis and y -axis taken together determine a plane known .
The coordinates of points in the XY-plane are of the form . (iii) Coordinate planes divide the space into octants. . Distance between Two Points We have studied about the distance between two points in two-dimensional coordinate system.
Let us now extend this study to three-dimensional system. Let P( x , y , z ) and Q ( x , y , z ) be two points referred to a system of rectangular axes OX, OY and OZ. Through