If the plane passing through the points $(1, 2, 3)$, $(2, 3, 1)$, and $(3, 1, 2)$ is $a x + b y + c z = 1$, then $a + 2 b + 3 c = $

In the following cases,determine whether the given planes are parallel or perpendicular,and in case they are neither,find the angles between them.
$2x - y + 3z - 1 = 0$ and $2x - y + 3z + 3 = 0$

The equation of the plane in normal form passing through the point $A(\vec{a})$, parallel to a vector $\vec{b}$ and containing a vector $\vec{c}$ is

Let $P$ be the plane passing through the point $(1, -1, -5)$ and perpendicular to the line joining the points $(4, 1, -3)$ and $(2, 4, 3)$. Then the distance of $P$ from the point $(3, -2, 2)$ is

If the plane $56x + 4y + 9z = 2016$ meets the coordinate axes at points $A$,$B$,and $C$,then the centroid of the $\triangle ABC$ is

The foot of the perpendicular drawn from the origin to the plane $x+y+3z-4=0$ is