The length of the perpendicular from the origin to the plane $\bar{r} \cdot (\hat{i} - 2\hat{j} + 3\hat{k}) = 14$ is

The equation of the plane,passing through the point $(1, 1, 1)$ and perpendicular to the planes $2x + y - 2z = 5$ and $3x - 6y - 2z = 7$,is

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

The combined equation for a pair of planes is $S \equiv 2 x^2-6 y^2-12 z^2+18 y z+2 z x+x y=0$. If one of the planes is parallel to $x+2 y-2 z=5$, then the acute angle between the planes $S=0$ is

In a tetrahedron $LMNO$,edges $ML, MN$ and $MO$ are mutually perpendicular. If the lengths of the altitudes drawn from $O, L$ and $N$ to their opposite faces are $1, 2$ and $3$ units respectively,then the length of the altitude drawn from $M$ to the face $LNO$ is:

If the foot of the perpendicular drawn from the origin to a plane is $P(2,-1,4)$,then the equation of the plane is