= Solution
At $\alpha=0$, $\Phi$ is the <orthogonal projection> onto the plane perpendicular to $n$. Its <image of a linear map> and <kernel of a linear map> are
$$
\boxed{\operatorname{im}\Phi=n^\perp,\qquad \ker\Phi=\operatorname{span}\{n\}.}
$$
Every perpendicular <vector> is unchanged and every parallel <vector> is annihilated. The image plane is perpendicular to the kernel axis by the definition of $n^\perp$; their dimensions two and one also agree with the <rank-nullity theorem>.
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