Find the point on the z-axis that is equidistant from the point A(1,-1,1) and B(1,0,-1). Then, find the point not on the z-axis that is equidistant from the point A and B.

Let P be the pointon the z-axis

|PA|=|PB|

Find P

let

(3-2z-z^2)^(0.5)=(2+2z+z^2)^(0.5)

solve y

y=0.25

Therefore point on z-axis is (0,0,0.25)

To find a point not on the z-axis, i found midpoint of a and b

Let that midpoint be Q so, (1,-0.5,0) is my answer.

Please check and let me know! thanks.