The point A has coordinates \((p, 1)\) and the point B has coordinates \((9, 3p + 1)\), where \(p\) is a constant.

(i) If the distance \(AB\) is 13 units, find the possible values of \(p\).

(ii) If the line with equation \(2x + 3y = 9\) is perpendicular to \(AB\), find the value of \(p\).