Where does the use of $ ext{LH}_2/ ext{LOX}$ provide the greatest advantage in a typical launch vehicle architecture?

Answer

In the vacuum environment of upper stages.

Hydrogen's high $I_{sp}$ is fully exploited in upper stages to maximize the final velocity change ($ ext{Delta V}$) delivered to the payload when operating in the vacuum of space.

Where does the use of $	ext{LH}_2/	ext{LOX}$ provide the greatest advantage in a typical launch vehicle architecture?
hydrogenfuelrocketpropellant