Solution
= Solution
The scalar product $\mathbf r\cdot\hat{\mathbf n}=d$ fixes the component of the <position vector> along the given <unit normal vector>. Thus the <locus> is \b[a plane normal to $\hat{\mathbf n}$], through $d\hat{\mathbf n}$. Its signed distance from the origin along that normal is $d$, and its perpendicular <distance> from the origin is $|d|$. Any <displacement> lying within the plane is <orthogonal> to $\hat{\mathbf n}$.