Question 6
In space, let $\Delta$ be a fixed line and $A$ a fixed point outside $\Delta$. A variable line $d$ rotates about $A$. Let $MN$ be the common perpendicular of $d$ and $\Delta$, with $M\in d$ and $N\in\Delta$. Find the locus of $M$ and the locus of the midpoint of $MN$.