Metric properties

Let $ABCDEFV$ be a regular hexagonal pyramid with a base edge length of $4\mathrm{cm}$ and a height of $8\mathrm{cm}$. Find the distance between the point $V$ and the line $BC$ (see the picture).

The cube $ABCDEFGH$ shown in the picture has edges of length $a=6\mathrm{cm}$. Find the distance between the point $B$ and the line $EG$.

The cube $ABCDEFGH$ shown in the picture has edges of length $a=6\mathrm{cm}$. Let $S_1$ be the midpoint of the diagonal $ED$ and let $S_2$ be the midpoint of the diagonal $CH$. Find the distance between the points $S_1$ and $S_2$.

The cube $ABCDEFGH$ shown in the picture has edges of length $a=6\mathrm{cm}$. Let $S$ be the midpoint of the base $ABCD$. Find the distance between the points $H$ and $S$.