Metric properties

The cube $ABCDEFGH$ shown in the picture has edges of length $a$. Find the distance between the lines $AB$ and $HG$.

The rectangular box $ABCDEFGH$ has sides of lengths $|AB|=6\mathrm{cm}$, $|BC|=4\mathrm{cm}$, $|AE|=8\mathrm{cm}$. Find the angle between the lines $AC$ and $SC$, where $S$ is the midpoint of the diagonal $EG$ (see the picture). Round the result to two decimal places.

The rectangular box $ABCDEFGH$ has sides of lengths $|AB|=6\mathrm{cm}$, $|BC|=4\mathrm{cm}$, $|AE|=8\mathrm{cm}$. Find the angle between the lines $HG$ and $AH$ (see the picture). Round the result to two decimal places.

The rectangular box $ABCDEFGH$ has sides of lengths $|AB|=6\mathrm{cm}$, $|BC|=4\mathrm{cm}$, $|AE|=8\mathrm{cm}$. Find the angle between the planes $ABC$ and $EFC$ (see the picture). Round the result to two decimal places.