Past exam of the mathematical methods I course of the University of Oxford / 2014 resit / 7

The common real variable gives the parametric equation of the line:Write $p=(2,-1,4)$ and $u=(1,3,2)$. The point closest to the origin is orthogonal to $u$, so $t_{\ast }=-p\cdot u/|u{|}^2=-7/14=-1/2$. Its position is $(3/2,-5/2,3)$. The distance from a point to a line in three dimensions is therefore