The locus represented by $xy + yz = 0$ is

If the equation of the plane bisecting the line segment joining the points $P(3,2,4)$ and $Q(-1,0,-2)$ and perpendicular to $PQ$ is $ax+by+cz+d=0$,then find the value of $ac+bd$.

$A$ point moves such that its distances from the points $(3, 4, -2)$ and $(2, 3, -3)$ remain equal. The locus of the point is

$A$ variable plane passes through a fixed point $(3, 2, 1)$ and meets the $x, y,$ and $z$ axes at $A, B,$ and $C$ respectively. $A$ plane is drawn parallel to the $yz$-plane through $A$,a second plane is drawn parallel to the $zx$-plane through $B$,and a third plane is drawn parallel to the $xy$-plane through $C$. Then,the locus of the point of intersection of these three planes is:

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x - y + 5z - 3 = 0$ are $ . . . . . . $.

The distance of the point $(2, -1, 0)$ from the plane $2x + y + 2z + 8 = 0$ is