The equation of the set of points which are equidistant from the points (1,2,3) and (3,2, - 1) is

Let the given points are A and B.Let P(x, y, z) be any point equidistant from A and B.PA = PB,i.e. Distance between P and A = distance between P and B⇒(x−1)2+(y−2)2+(z−3)2=(x−3)2+(y−2)2+(z+1)2.⇒ (x−1)2+(y−2)2+(z−3)2=(x−3)2+(y−2)2+(z+1)2⇒ x2+1−2x+y2+4−4y+z2+9−6z         =x2+9−6x+y2+4−4y+z2+1+2z⇒  4x−8z=0⇒  x−2z=0which is the required equation.