Consider a straight line k and a point P that does not lie on k.
a. (i) Show that at least one straight line can be drawn through P that is perpendicular to k.
b. (ii) Prove that no two distinct straight lines through P can both be perpendicular to k.
c. (iii) Combine the above results to conclude that exactly one perpendicular can be drawn from an external point to a given line.