The equation of the plane passing through the origin and perpendicular to the planes $x+2y-z=1$ and $3x-4y+z=5$ is:

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

If the perpendicular distance from $(1, 2, 4)$ to the plane $2x + 2y - z + k = 0$ is $3$,then $k =$

If the point $(2, \alpha, \beta)$ lies on the plane which passes through the points $(3, 4, 2)$ and $(7, 0, 6)$ and is perpendicular to the plane $2x - 5y = 15$,then $2\alpha - 3\beta$ is equal to:

$A$ line joining the points $(1, 2, 0)$ and $(4, 13, 5)$ is perpendicular to a plane. Then the coefficients of $x, y$ and $z$ in the equation of the plane are respectively

$A$ plane passes through the point $A(2, 1, -3)$. If the distance of this plane from the origin is maximum,then its equation is