If the foot of the perpendicular drawn from the origin to a plane is $(1, 2, 3)$,then a point on that plane 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 $P$?

If $O$ is the origin and $A$ is the point $(a, b, c)$,then the equation of the plane passing through $A$ and perpendicular to $OA$ is:

The volume of the tetrahedron (in cubic units) formed by the plane $2x + y + z = K$ and the coordinate planes is $\frac{2V^3}{3}$,then $K:V =$

If the mirror image of the point $(2, 4, 7)$ in the plane $3x - y + 4z = 2$ is $(a, b, c)$,then $2a + b + 2c$ is equal to

$A$ plane meets the coordinate axes at $A, B, C$ such that the centroid of the $\Delta ABC$ is the point $(\alpha, \beta, \gamma)$. Show that the equation of the plane is $\frac{x}{\alpha} + \frac{y}{\beta} + \frac{z}{\gamma} = 3$.