Recall that for a given segment AB in the plane, its perpendicular bisector is the line that passes through the midpoint of AB and is perpendicular to it. It has been established in class, that this is precisely of points that are equidistant1 from A and B. The exercise addresses the analogous question for a segment AB in R 3 .

(a) Let A = (xA, yA, zA) and B = (xB, yB, zB) be two points in R 3 . Show that the set of points in R 3 that are equidistant from A and B is a plane. Give an equation of this plane, in terms of the coordinates of A and B.

(b) Application. Find the equation of the plane formed by the points that are at equal distance from A = (3, 5, 2) and B = (1, 1, 4).