The equations $x + y + z + 2 = 0$ and $x + y + z + 3 = 0$ together represent what in space?

If $A(-1, 2, 3)$,$B(1, 1, 1)$ and $C(2, -1, 3)$ are points on a plane,then a unit normal vector to the plane $ABC$ is:

If from a point $P(a, b, c)$ perpendiculars $PA$ and $PB$ are drawn to the $yz$-plane and $zx$-plane respectively,then the equation of the plane $OAB$ (where $O$ is the origin) is:

$A$ variable plane is at a distance of $6$ units from the origin. If it meets the coordinate axes in $A, B$, and $C$, then the equation of the locus of the centroid of the $\triangle ABC$ is

The perpendicular distance from the origin to the plane containing the points $A(1, -2, 1)$, $B(2, -1, -3)$ and $C(0, 1, 5)$ is (in units)

If a plane cuts off intercepts $-6, 3, 4$ from the coordinate axes,then the length of the perpendicular from the origin to the plane is