Solution
= Solution
The common real <variable> gives the <parametric equation> of the <line>:
$$
\boxed{\mathbf r=(2,-1,4)+t(1,3,2),\qquad t\in\mathbb R.}
$$
Write $p=(2,-1,4)$ and $u=(1,3,2)$. The point closest to the origin is <orthogonal> to $u$, so $t_*=-p\cdot u/|u|^2=-7/14=-1/2$. Its position is $(3/2,-5/2,3)$. The <distance from a point to a line in three dimensions> is therefore
$$
\boxed{d=\sqrt{|p|^2-\frac{(p\cdot u)^2}{|u|^2}}=\sqrt{\frac{35}{2}}=\frac{\sqrt{70}}2.}
$$