Perpendicular bisector plane

Plane bisecting segment joining $$A(x_1,y_1,z_1)$$ and $$B(x_2,y_2,z_2)$$ at right angles:

$$ (x_2 - x_1)(x - \frac{x_1+x_2}{2}) + (y_2 - y_1)(y - \frac{y_1+y_2}{2}) + (z_2 - z_1)(z - \frac{z_1+z_2}{2}) = 0 $$

Simplified: $$ 2(x_2 - x_1)x + 2(y_2 - y_1)y + 2(z_2 - z_1)z = x_2^2 + y_2^2 + z_2^2 - x_1^2 - y_1^2 - z_1^2 $$