The equation of the plane passing through the points $(-1, 2, -2)$ and $(-1, 3, 2)$ and perpendicular to the $yz$-plane is:

The distance of a point $(1, 2, -1)$ from the plane $x - 2y + 4z + 10 = 0$ is

The plane $ax + by + cz = 1$ meets the coordinate axes at points $A, B$,and $C$. Find the centroid of the triangle $ABC$.

$A$ point lying on the plane that passes through the points $\hat{i}-\hat{j}+\hat{k}$, $\hat{i}-2\hat{j}+3\hat{k}$, and $\hat{i}+2\hat{j}-3\hat{k}$ is:

The equation of the plane,passing through the midpoint of the line segment joining the points $P(1, 2, 5)$ and $Q(3, 4, 3)$ and perpendicular to it,is

In a tetrahedron $LMNO$,edges $ML, MN$ and $MO$ are mutually perpendicular. If the lengths of the altitudes drawn from $O, L$ and $N$ to their opposite faces are $1, 2$ and $3$ units respectively,then the length of the altitude drawn from $M$ to the face $LNO$ is: