VMO 1979 Problem 6

$ABCD$ is a rectangle with $BC / AB = \sqrt2$ . $ABEF$ is a congruent rectangle in a different plane. Find the angle $DAF$ such that the lines $CA$ and $BF$ are perpendicular. In this configuration, find two points on the line $CA$ and two points on the line $BF$ so that the four points form a regular tetrahedron.