conversely, given a triplet of three numbers ( x, y, z ), how, we locate a point in the space. Given a point P in space, we drop a perpendicular PM on the XY-plane with M as the foot of this perpendicular (Fig . ). Then, from the point M, we draw a perpendicular ML to the x- axis, meeting it at L.
Let OL be x , LM be y and MP be z. Then x,y and z are called the x , y and z coordinates , respectively, of the point P in the space. In Fig . , we may note that the point P ( x , y , z ) lies in the octant XOYZ and so all x , y , z are positive.
If P was in any other octant, the signs of x , y and z would change Fig . Fig . MATHEMATICS accordingly. Thus, to each point P in the space there corresponds an ordered triplet ( x , y , z ) of real numbers.
Conversely, given any triplet ( x , y , z ), we would first fix the point L on the x -axis corresponding to x , then locate the point M in the XY-plane such that ( x , y ) are the coordinates of the point M in the XY-plane. Note that LM is perpendicular to the x- axis or is parallel to the y -axis. Having reached the point M, we draw a perpendicular MP to the XY-plane and locate on it the point P corresponding to z . The point P so obtained has then the coordinates ( x , y , z ).
Thus, there is a one to one correspondence between the points in space and ordered triplet ( x , y , z ) of real numbers. Alternatively, through the point P in the space, we draw three planes parallel to the coordinate planes, meeting the x -axis, y -axis and z -axis in the points A, B and C, respectively (Fig . ). Let OA = x , OB