(688,#27) Find an equation of the set of all points equidistant from the points A(-1,5,3) and B(6,2,-2).

Solution:

We need a set of points P where .

Distance formula in three dimensions for the distance between the points

is:

The set of points (x,y,z) satisfying this last equation is the set of points P equally distant from the two given points.

by:sh