The angle of elevation of the top of a tower from a point \( A \) due north of it is \( \alpha \) and from a point \( B \) at a distance of \( 9 \) units due west of \( A \) is \( \cos^{-1}\!\left(\dfrac{3}{\sqrt{13}}\right) \). If the distance of the point \( B \) from the tower is \( 15 \) units, then \( \cot \alpha \) is equal to:
