Find the equation of the plane passing through the point $(\alpha, \beta, \gamma)$ and parallel to the plane $x + y + z = 0$.

The equation of the plane passing through the points $(-1, -2, 0)$ and $(2, 3, 5)$ and parallel to the line $r = -3j + k + \lambda(2i + 5j - k)$ is

$A$ variable plane $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$,which is at a unit distance from the origin,cuts the coordinate axes at $A, B$,and $C$. If the centroid $(x, y, z)$ of $\triangle ABC$ satisfies $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=k$,then $k$ equals:

The foot of the perpendicular drawn from the origin to the plane is $(4, -2, -5)$. Hence,the equation of the plane is

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

Equations of planes parallel to the plane $x-2y+2z+4=0$ which are at a distance of $1$ unit from the point $(1, 2, 3)$ are $.....$