4. Find the equation of the set of points which are equidistant from the points (1, 2, 3) and (3, 2, –1).
Given two points, A = (1, 2, 3) and B = (3, 2, -1).
Let the point P= (x,y,z) be a point which is equidistance equilibrium with the points A and B.
so,
The distance PA = The distance PB
Now let's apply the simplification property.
Hence, the locus of the point which is equidistant from A and B is .