I have two given points. A=(-1,2,3) and B=(3,4,-3). I want to find all points (x1,x2,x3) that have the same distance to A and B. Attempt: I think finding the line they both lie on is a good first step. To do this, I've drawn a vector between A and B, and found the line's equation. L=(3,4,-3)+t(2,1,-3). I've come to the conclusion that I have to find a perpendicular bisector of some sort. And I guess cross product wont work, cause I only have one line(?). What is the next step?