The value of $k$ for which the planes $3x - 6y - 2z = 7$ and $2x + y - kz = 5$ are perpendicular to each other,is

$A$ plane $P$ is parallel to two lines whose direction ratios are $-2, 1, -3$ and $-1, 2, -2$,and it contains the point $(2, 2, -2)$. Let $P$ intersect the coordinate axes at the points $A, B, C$ making the intercepts $\alpha, \beta, \gamma$. If $V$ is the volume of the tetrahedron $OABC$,where $O$ is the origin and $p = \alpha + \beta + \gamma$,then the ordered pair $(V, p)$ is equal to.

If the foot of the perpendicular from $(0,0,0)$ to a plane is $(1,2,3)$,then the equation of the plane is

The length of the foot of the perpendicular from the point $P\left(1, \frac{3}{2}, 2\right)$ to the plane $2x - 2y + 4z + 17 = 0$ is

The equation of a plane containing the point $(1, -1, 2)$ and perpendicular to the planes $2x + 3y - 2z = 5$ and $x + 2y - 3z = 8$ is

In each of the following cases,determine the direction cosines of the normal to the plane and the distance from the origin.
$Z=2$