(0,0,0),( a , 0,0),(0, ~b , 0) and (0,0, c ) are four distinct points. What are the coordinates of the point which is equidistant from the four points?

Step-by-step solution

A (0,0,0), B ( a , 0,0), C (0, ~b , 0), D (0,0, c ) Let the equidistant point be P ( x , y , z ) aligned & i.e, A P=B P, A P=C P, A P=D P & (x-0)^2+(y-0)^2+(z-0)^2 & = (x-a)^2+y^2+z^2 & x^2+y^2+z^2=(x-a)^2+y^2+z^2 & x^2=x^2-2 a x+a^2 & a^2-2 a x=0 & a(a-2 x)=0 aligned Since a 0, a=2 x x= a 2 Similarly, we will get y = b 2 , z = c 2