1. The problem statement, all variables and given/known data Show that the points in R3 equidistant from two fixed points, p and q, form a plane and find the equation of the plane. 2. Relevant equations 3. The attempt at a solution So the equation of the plane takes the form ax + by+ cz = d, where (a,b,c) is a normal vector of the plane. assuming p = (x1, y1, z1) and q = (x2, y2, z2), how can i show that the points equidistant from both these points is a plane? It doesn't really make sense to me visually I mean. The only way i can think of a point being equidistant is if its on a line in the middle of the two points. Its like an equilateral triangle, where if p and q were bottom left and right corners and the point on the top is equidistant from both, if it wasn't in the middle then the distance to one of the points will be greater than the distance to the other. Hopefully someone understands what I mean.