Let P (x, y, z) be the point that is equidistant from points A(1, 2, 3) and B(3, 2, –1). Accordingly, PA = PB
⇒ PA2 = PB2
⇒(X - 1)2 + ( y - 2)2 (z - 3)2 = (x - 3)2 + (z + 1)2
⇒ x2 – 2x + 1 + y2 – 4y + 4 + z2 – 6z + 9 = x2 – 6x + 9 + y2 – 4y + 4 + z2 + 2z + 1
⇒ –2x –4y – 6z + 14 = –6x – 4y + 2z + 14
⇒ – 2x – 6z + 6x – 2z = 0
⇒ 4x – 8z = 0
⇒ x – 2z = 0
Thus, the required equation is x – 2z = 0.