The equation of the plane which is parallel to the $y$-axis and cuts off intercepts of length $2$ and $3$ from the $x$-axis and $z$-axis respectively is:

Consider three planes:
$P_1: x-y+z=1$
$P_2: x+y-z=-1$
$P_3: x-3y+3z=2$
Let $L_1, L_2, L_3$ be the lines of intersection of the planes $P_2$ and $P_3$,$P_3$ and $P_1$,and $P_1$ and $P_2$,respectively.
$STATEMENT-1$: At least two of the lines $L_1, L_2$ and $L_3$ are non-parallel.
$STATEMENT-2$: The three planes do not have a common point.

If the planes $3x - 2y + 2z + 17 = 0$ and $4x + 3y - kz = 25$ are mutually perpendicular,then $k = $

If the foot of the perpendicular from $(0,0,0)$ to the plane is $(1,2,2)$,then the equation of the plane is

If the foot of the perpendicular from $(0,0,0)$ to a plane is $(1,2,3)$,then the equation of the plane is

If the plane $\frac{x}{2} + \frac{y}{3} + \frac{z}{3} = 1$ intersects the coordinate axes at $A, B, C$,then the area of $\Delta ABC$ is: