Distance between the two planes: $2x + 3y + 4z = 4$ and $4x + 6y + 8z = 12$ is

From a point $P(a, b, c)$, perpendiculars $PA$ and $PB$ are drawn to $XY$ plane and $ZX$ plane respectively. If $O$ is the origin, then the equation of plane $OAB$ is

$A$ 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 $d =$

If $O$ is the origin and the coordinates of $P$ are $(1, 2, -3),$ find the equation of the plane passing through $P$ and perpendicular to $OP.$

The equation of the plane passing through the midpoint of the line segment joining the points $A(4, 5, -10)$ and $B(-1, 2, 1)$ and perpendicular to $AB$ is:

$A$ plane is parallel to two lines whose direction ratios are $2, 0, -2$ and $-2, 2, 0$ and it contains the point $(2, 2, 2)$. If it cuts the coordinate axes at $A, B, C$,then the volume of the tetrahedron $OABC$ (in cubic units) is