Let A(x, y, z) be any point which is equidistant from points B(1, 2, 3) and C(3, 2, –1). Then AB = $\sqrt{(x-1)^2+(y-2)^2+(z-3)^2}$ AC = $\sqrt{(x-3)^2+(y-2)^2+(z+1)^2}$ It is given that AB = AC $\sqrt{(x-1)^2+(y-2)^2+(z-3)^2}$ = $\sqrt{(x-3)^2+(y-2)^2+(z+1)^2}$ ⇒ $(x-1)^2+(y-2)^2+(z-3)^2$ = $(x-3)^2+(y-2)^2+(z+1)^2$ ⇒ $x^2$ + 1 - 2x + $z^2$ + 9 - 6z = $x^2$ + 9 - 6x + $z^2$ + 1 + 2z ⇒ - 2x - 6z + 10 = - 6x + 2z + 10 ⇒ - 2x - 6z + 6x - 2z = 0 ⇒ 4x - 8z = 0 ⇒ x - 2z = 0