= Solution
This plane contains the direction $\mathbf b-\mathbf a$ and is parallel to $\mathbf c$. Put $\mathbf N=(\mathbf b-\mathbf a)\times\mathbf c$. Its <scalar triple product> with $\mathbf a$ is again $D\ne0$, proving $\mathbf N\ne0$. Hence
$$
\boxed{\mathbf n=\frac{(\mathbf b-\mathbf a)\times\mathbf c}{|(\mathbf b-\mathbf a)\times\mathbf c|},\qquad \mu=\frac D{|(\mathbf b-\mathbf a)\times\mathbf c|}.}
$$
The <dot product> with $\mathbf c$ vanishes, while the <dot products> with $\mathbf a$ and $\mathbf b$ equal $\mu$ after normalization. These verify both incidence and parallelism.
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