= Solution
<planar anchoring> favors the <nematic director> tangent to a surface. A flat wall at $z=0$ permits uniform $\mathbf n=\hat{\mathbf x}$, as in the sketch. A rubbed surface can select one in-plane axis; degenerate <planar anchoring> selects only the tangent plane.
For the degenerate case, $f_s=(W/2)(\mathbf n\cdot\boldsymbol\nu)^2$ has minima at $\mathbf n\cdot\boldsymbol\nu=0$. A remote incompatible boundary produces elastic distortion. \b[Tangency alone does not specify an azimuthal direction within the surface.]
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