the easiest way to do 10 is to get |a+b+c|^2 = (a+b+c).(a+b+c) = 3 + 2a.c
so a.(a+b+c) = |a||a+b+c|cos(t) --> 1+a.c = sqrt(3+2a.c)cos(t) --> cos(t) = (1+a.c)/sqrt(3+2a.c).
Now if a = c, then cos(t) = 2/sqrt(5) which is biggest value cos(t) can be under this restriction, thus the smallest angle...