The Cartesian equation of the plane $r = (1 + \lambda - \mu )i + (2 - \lambda )j + (3 - 2\lambda + 2\mu )k$ is

$A$ variable plane passes through a fixed point $(3, 2, 1)$ and meets the $x, y,$ and $z$ axes at $A, B,$ and $C$ respectively. $A$ plane is drawn parallel to the $yz$-plane through $A$,a second plane is drawn parallel to the $zx$-plane through $B$,and a third plane is drawn parallel to the $xy$-plane through $C$. Then,the locus of the point of intersection of these three planes is:

If $a, b, c$ are the intercepts made on $X, Y, Z$-axes respectively by the plane passing through the points $(1, 0, -2), (3, -1, 2)$ and $(0, -3, 4)$,then $3a + 4b + 7c =$

If $(2, -3, 6)$ is the foot of the perpendicular drawn from the origin to a plane,then the equation of that plane is

The vector equation of a plane,which is at a distance of $8$ units from the origin and which is normal to the vector $\vec{n} = 2\hat{i} + \hat{j} + 2\hat{k}$,is

The distance of a point $(1, 2, -1)$ from the plane $x - 2y + 4z + 10 = 0$ is