The shortest distance between the lines $\dfrac{x - 3}{3} = \dfrac{y - 8}{-1} = \dfrac{z - 3}{1}$ and $\dfrac{x + 3}{-3} = \dfrac{y + 7}{2} = \dfrac{z - 6}{4}$ is

A plane meets the co-ordinate axes in A, B, C such that the centroid of the triangle ABC is the point $(1, r, r^2)$, then the equation of the plane is,

If M denotes the midpoint of the line joining A$(4, 5, -10)$ and B$(-1, 2, 1)$, then the equation of the plane through M and perpendicular to AB is:

The perpendicular distance from the origin to the plane containing the points $(1, -2, 1), (2, -1, -3)$ and $(0, 1, 5)$ is...(in units)