= Solution
Write $\mathbf r=\mu\mathbf n+\mathbf v$. Since $\mathbf n$ is a <unit vector>, the equation becomes $\mathbf v\cdot\mathbf n=0$. Thus $\mathbf v$ ranges over the two-dimensional <orthogonal complement> of $\mathbf n$: the locus is an <affine hyperplane> through $\mu\mathbf n$, with <unit normal> $\mathbf n$. Conversely, every such vector satisfies the equation. Its perpendicular distance from the origin is $\boxed{|\mu|}$; $\mu$ is the signed distance in the chosen normal direction.
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