For scalars $\lambda, \mu$, if the vector equation of a plane is $r=(2+3 \lambda-\mu) \hat{i}+(1-2 \lambda+3 \mu) \hat{j}+(-2+2 \lambda+\mu) \hat{k}$, then its Cartesian equation is

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x - 3y + 4z = 29$ are

The mirror image of the point $(1, 2, 3)$ in a plane is $\left(-\frac{7}{3}, -\frac{4}{3}, -\frac{1}{3}\right)$. Which of the following points lies on this plane?

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

The Cartesian equation of a plane which passes through the points $A(2,2,2)$ and makes equal non-zero intercepts on the coordinate axes is