Question

Find the coordinates of a point equidistant from the four point O (0, 0, 0), A (a, 0, 0), B (0, b, 0) and C (0, 0, c).

Answer 1

Let P(x,y,z) be the desired point.Then OP=PA=PB=PCNow, OP=PA�OP2=PA2�x2+y2+z2=(x�a)2+(y�0)2+(z�0)2�x=a2Similarly, OP=PB�y=b2 and OP=laptop�z=c2Hence, the cordinate of the required point are (a2,b2,c2)
Regards

Answer 2

Example 1 Locate the points (i) (2, 3, 4) (ii) (–2, –2, 3) in space. Solution (i) To locate the point (2, 3, 4) in space, we move 2 units from O along the positive direction of x-axis. Let this point be A (2, 0, 0). From the point A moves 3 units parallel to +ve direction of y-axis.Let this point be B (2, 3, 0). From the point B moves 4 units along positive direction of z-axis. Let this point be P (2, 3, 4) Fig.(12.3). Fig. 12.3 INTRODUCTION TO THREE DIMENSIONAL GEOMETRY 211 (ii) From the origin, move 2 units along the negative direction of x-axis. Let this point be A (–2, 0, 0). From the point A move 2 units parallel to negative direction of y-axis. Let this point be B (–2, –2, 0). From B move 3 units parallel to positive direction of z - axis. This is our required point Q (–2, –2, 3) (Fig.12.4.)