Calculus Question HELP!?

The only way |a+b| would equal |a| + |b| is if the direction of a and b are the same. Otherwise, they are not aligned and the magnitude of the sum of the two vectors will be less than the sum of the individual vector magnitudes. Similarly, there is no possible way that |a+b| would be greater than |a| + |b| since the best you can do is equality (when both vectors are aligned).