The length of arrow b would be smaller if a catalyst is added.
Arrow b represents the activation energy. It is the minimum energy the reactants of a reaction need to surmount to have a chance of arriving at products. The higher this energy, the slower the rate of reactions.
The addition of catalysts to reactions helps lower the activation energy of reactions, thereby speeding up the rate of reactions. This means that the reactants will be able to reach products at a faster rate.
Thus, the introduction of a catalyst to the reaction shown by the image will lead to a reduction in the length of arrow b, since this arrow depicts the activation energy of the reaction.