Question

Find an equation for the plane consisting of all points that are equidistant from the given points.
(-6, 1, 2), (4, 3, 6).

Answer 1

Let P(-6,1,2) and Q(4,3,6) i think the you have the formula to get the middle point of PQ.
and think about it in R^2 PQ is normal vector of the requirement plane.
You have a point, a normal vector, equation of the plane is easy to write out. i just give you the idea, the leftover is your responsibility.