The length of the perpendicular from the origin to the plane $3x + 4y + 12z = 52$ is

$A$ plane meets the coordinate axes at the points $A, B, C$ respectively in such a way that the centroid of $\triangle ABC$ is $(1, r, r^2)$ for some real $r$. If the plane passes through the point $(5, 5, -12)$,then $r=$

Find the equation of the plane passing through the point $(1, 2, 3)$ and parallel to the plane $2x + 3y - 4z = 0$.

$A$ plane ( $\pi$ ) passing through the point $(1, 2, -3)$ is perpendicular to the planes $x + y - z + 4 = 0$ and $2x - y + z + 1 = 0$. If the equation of the plane ( $\pi$ ) is $ax + by + cz + 1 = 0$,then $a^2 + b^2 + c^2 =$

$A$ plane $\pi$ given by $ax + by + 11z + d = 0$ is perpendicular to the planes $2x - 3y + z = 4$ and $3x + y - z = 5$. The perpendicular distance from the origin to the plane $\pi$ is $\sqrt{6}$ units. If all the intercepts made by the plane $\pi$ on the coordinate axes are positive,then $d =$

$A$ variable plane is at a constant distance $h$ from the origin and meets the coordinate axes in $A, B, C$. The locus of the centroid of $\triangle ABC$ is