I'm having a problem of finding the origin $O(x,y,z)$ of 2 3D points $P_1 (1,2,2)$ and $P_2 (2,3,5)$, distance $OP_1 = OP_2$, angle = 60 degrees and Plane Equation: $$E: 1.15714286x + 1.8547619y-z-2.86101191=0.$$ I used the distance equation, plane equation, and cross vector of products but I found 2 origin $O_1$ and $O_2$. I don't know which one I should choose to correct my answer.
Are there any ways to identify it?
The problem has indeed two solutions. You can't differentiate them if you don't provide an additional information. Orientation of the plane can be one.