Find the perpendicular foot and reflect a point

Given three points $A(0,2,7)$, $B(5,-3,2)$ and $C(1,1,1)$, find the position vector of the point $R$ on $AB$ such that $CR$ is perpendicular to $AB$. Hence find the perpendicular distance from $C$ to $AB$ and the position vector of the reflection of $C$ in $AB$.