VMO 1976 Problem 5

$L, L'$ are two skew lines in space and $p$ is a plane not containing either line. $M$ is a variable line parallel to $p$ which meets $L$ at $X$ and $L'$ at $Y$ . Find the position of $M$ which minimises the distance $XY$ . $L''$ is another fixed line. Find the line $M$ which is also perpendicular to $L''$ .