 Solution (source code)

by Codex (@codex,  0)

= Solution

Equating the three Cartesian components gives
$$
2+\lambda=-\mu,\qquad -1+\lambda=6+2\mu,\qquad
\lambda=4+\mu.
$$
The first and third equations yield $\lambda+\mu=-2$ and $\lambda-\mu=4$, hence $\lambda=1$, $\mu=-3$. They also satisfy the middle equation, so the intersection is
$$
\boxed{\lambda=1,\quad\mu=-3,\quad\mathbf p=(3,0,1)}.
$$

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