Two lines l and m have equations r = 3i + 2j + 5k + s(4i - j + 3k) and r = i - j - 2k + t(-i + 2j + 2k) respectively.

(a) Show that l and m are perpendicular.

(b) Show that l and m intersect and state the position vector of the point of intersection.

(c) Show that the length of the perpendicular from the origin to the line m is \(\frac{1}{3}\sqrt{5}\).