$A$ plane meets the coordinate axes at points $A, B$,and $C$ such that the centroid of $\Delta ABC$ is $(1, 2, 3)$. The equation of the plane is

The equation of the plane passing through $(1, 1, 1)$ and $(1, -1, -1)$ and perpendicular to $2x - y + z + 5 = 0$ is:

Let $P$ be the plane passing through the points $(5,3,0), (13,3,-2)$ and $(1,6,2)$. For $\alpha \in N$,if the distances of the points $A(3,4,\alpha)$ and $B(2,\alpha,a)$ from the plane $P$ are $2$ and $3$ respectively,then the positive value of $a$ is:

The volume (in cubic units) of the tetrahedron bounded by the plane $3x + 4y - 5z = 60$ and the three coordinate planes is

If $(2,3,-1)$ is the foot of the perpendicular from $(4,2,1)$ to a plane,then the equation of the plane is

$A$ plane which is perpendicular to two planes $2x - 2y + z = 0$ and $x - y + 2z = 4$ passes through $(1, 2, 1)$. The distance of the plane from the point $(2, 3, 4)$ is