Question

Question
Find an equation of the set of all points equidistant from the points
A(−2, 5, 2) and B(5, 1, −3).

Answer 1

Think of two points in space.

The set of all points equidistant from the points is therefore a plane that separates the two points, right in the middle.

Also the line joining the two points would be perpendicular to the plane.

The mid-point between the two points would evidently lie on the plane.

(1) Find the mid-point between the two given points using the mid-point formula. Let this be p0.
(2) Find the vector AB joining the two given points. Then AB is the normal vector to the plane we're looking for.
Let AB=<a,b,c>
(3) Use the components of the normal vector AB (a,b,c) to form the equation of the required plane:
a(x-x0)+b(y-y0)+c(z-z0)=0
where (x0,y0,z0) is the mid-point P0 between A and B.

If you need more details, please post.