The coordinates of the foot of the perpendicular drawn from the origin to the plane $2x - 3y + 4z = 29$ are

If the planes $x + 2y + kz = 0$ and $2x + y - 2z = 0$ are at right angles,then the value of $k$ is

If $M$ is the foot of the perpendicular drawn from $P(1, 2, -1)$ to the plane passing through the point $A(3, -2, 1)$ and perpendicular to the vector $\vec{n} = 4\hat{i} + 7\hat{j} - 4\hat{k}$,then the length of $PM$,in proper units,is

$\pi_1$ is a plane passing through the point $(1, 2, 3)$ and perpendicular to the planes $x+2y+3z-6=0$ and $x+2y+2z-5=0$. If $(-1, 2, -3)$ is the foot of the perpendicular drawn from the point $(1, 3, 2)$ onto a plane $\pi_2$, then the angle between the planes $\pi_1$ and $\pi_2$ is

If a plane passes through $(1, -2, 1)$ and is perpendicular to the planes $2x - 2y + z = 0$ and $x - y + 2z = 4$,then the distance of that plane from the point $(1, 2, 2)$ is

$A$ tetrahedron has vertices $P(1,2,1), Q(2,1,3), R(-1,1,2)$ and $O(0,0,0)$. Then the angle between the faces $OPQ$ and $PQR$ is