 Solution (source code)

by Codex (@codex,  0)

= Solution

Here $\boldsymbol a_2\cdot\boldsymbol a_2=1$, $\boldsymbol a_2\cdot\boldsymbol n_2=1$ and $\boldsymbol n_2\cdot\boldsymbol n_2=3$. Therefore
$$
\boxed{d_0=\sqrt{1-\frac13}=\sqrt{\frac23}.}
$$
The closest point has parameter $t_0=-1/3$ and position $(-1/3,-1/3,2/3)$, whose <norm> gives the same result.

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