In a school, the swimming pool is shaped as a cuboid, and the breadth of the pool is represented by line $\frac{-x + 2}{-5} = y = z - 3$. Two students A and B are swimming along the length of the pool. Based on the above information, answer the following questions : (i) If the path of student A is represented by line $\frac{x + 5}{1} = \frac{y + 3}{4} = \frac{z - 6}{-3p}$, find the value of p. (ii) Write the vector equation of the path of student B swimming parallel to the path of student A, if at a certain instant he passes through the point with coordinates $(2, 4, -1)$. (iii) (a) Find the foot of the perpendicular drawn from $(2, 4, -1)$ to the path represented by student A. OR (iii) (b) If a bird flies across the top of the swimming pool with its path represented by $\frac{x + 4}{2} = \frac{y + 3}{8} = \frac{z - 5}{-18}$, then find the shortest distance between its path and the path of student A.