If the cartesian equation of the plane passing through the point $\hat{i}+2 \hat{j}+\hat{k}$ and parallel to the vectors $2 \hat{i}+3 \hat{j}+\hat{k}$ and $-\hat{i}+2 \hat{j}-3 \hat{k}$ is $a x+b y+c z=1$, then $18(a+b+c)$ is equal to

If the angle between the planes $\bar{r} \cdot(11 \hat{i}-2 \hat{j}+\alpha \hat{k})=7$ and $\bar{r} \cdot(2 \hat{i}+4 \hat{j}-2 \hat{k})=5$ is $\frac{\pi}{2}$, then $\alpha=$

The equation of the plane passing through the points $(2,1,0)$,$(3,2,-2)$,and $(3,1,7)$ is

The distance between the planes $x + 2y + 3z + 7 = 0$ and $2x + 4y + 6z + 7 = 0$ is

The foot of the perpendicular from the origin $O$ to a plane $P$,which meets the coordinate axes at points $A, B, C$,is $(2, a, 4)$,where $a \in N$. If the volume of the tetrahedron $OABC$ is $144 \text{ unit}^3$,then which of the following points does $NOT$ lie on the plane $P$?

The distance between the parallel planes $2x - 2y + z + 3 = 0$ and $4x - 4y + 2z + 5 = 0$ is: