The equation of the plane whose intercepts on $x, y, z$ axes are $1, 2, 4$ respectively is

The equation of the plane passing through $(4,4,0)$ and perpendicular to the planes $2x+y+2z+3=0$ and $3x+3y+2z-8=0$ is

Find the equation of the plane passing through the intersection of the planes $\vec{r} \cdot (\hat{i} + 3\hat{j} - \hat{k}) = 5$ and $\vec{r} \cdot (2\hat{i} - \hat{j} + \hat{k}) = 3$,and passing through the point $(2, 1, -2)$.

$A$ plane passes through the points $A (1, 2, 3)$,$B (2, 3, 1)$,and $C (2, 4, 2)$. If $O$ is the origin and $P$ is $(2, -1, 1)$,then the projection of $\overline{OP}$ on this plane is of length .... .

The perpendicular distance of the point $(1, -1, 2)$ from the plane $x + 2y + z = 4$ 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