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

The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x + 6y - 3z = 63$ are

If ${P_1}$ and ${P_2}$ are the lengths of the perpendiculars from the points $(2, 3, 4)$ and $(1, 1, 4)$ respectively to the plane $3x - 6y + 2z + 11 = 0$,then ${P_1}$ and ${P_2}$ are the roots of the equation:

The angle between the planes $\vec{r} \cdot(2 \hat{i}+4 \hat{j}-3 \hat{k})=5$ and $\vec{r} \cdot(5 \hat{i}+3 \hat{j}+4 \hat{k})=7$ is

If $(2,3,-1)$ is the foot of the perpendicular from $(4,2,1)$ to a plane,then the equation of the plane is

The plane passing through the points $(1,1,1)$,$(1,-1,1)$ and $(-7,-3,-5)$ is