Solution
= Solution
Use the <distance from a point to a plane> formula with the <unit normal> $\hat{\mathbf n}$. Since the <plane> passes through the origin, the distance is
$$
\boxed{d=|\mathbf p\cdot\hat{\mathbf n}|=\frac{|2+0|}{\sqrt2}=\sqrt2}.
$$
For a direct check, the <closest point on a plane> is $\mathbf p-(\mathbf p\cdot\hat{\mathbf n})\hat{\mathbf n}=(1,\sqrt2,-1)^T$, whose displacement from $\mathbf p$ has <Euclidean norm> $\sqrt2$.