Relative to an origin O, the position vectors of points A and B are given by

\(\overrightarrow{OA} = \begin{pmatrix} 5 \\ 1 \\ 3 \end{pmatrix}\) and \(\overrightarrow{OB} = \begin{pmatrix} 5 \\ 4 \\ -3 \end{pmatrix}\).

The point P lies on AB and is such that \(\overrightarrow{AP} = \frac{1}{3} \overrightarrow{AB}\).

(i) Find the position vector of P.

(ii) Find the distance OP.

(iii) Determine whether OP is perpendicular to AB. Justify your answer.