Question -
Answer -
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
⇒ 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 requiredequation is x – 2z = 0.