Find a perpendicular foot, shortest distance and reflected point

The point is $P=(1,1,-1)$ and the line is $\mathbf r=(1,2,3)+\lambda(1,2,1)$, $\lambda\in\mathbb R$.

(i) Find the coordinates of the foot of the perpendicular from P to the line.

(ii) Deduce the shortest distance from P to the line.

(iii) Find the position vector of the image of P in the line.