(I just typed this up real quick so idk if i made a mistake or not I will relook through it now, hopefully this makes sense)
So, when the magnitude of (p + q) is a minimum is when q is antiparallel to p (which just means that p is parallel to q but they point in opposing directions), as you would have seen in (i). So, since the magnitude of q is 20, then q = -20(p̂) = -(20/17)p. So, a = p + q = p -(20/17)p = -(3/17)p which can easily be calculated since that they gave u what p is.
(just to clarify: 17 is the magnitude of p)
