Their common name comes from the distinctive brick red tail that makes most of them easy to identify in the wild. Red-tailed hawks are large, sturdy raptors with a short tails, broad secondary flight feathers for soaring and strong feet for capturing prey. But that was a very young, emaciated bird desperate for food and not typical of most red-tails.
That being said, as a rehabilitator, I did pick up a hawk that a farmer captured after it killed one of his chickens. They're often called chicken hawks but a full sized chicken is a bit too big for a red-tail. Red-tailed hawks typically hunt small mammals from mice to squirrels and rabbits but also take snakes and birds, like pigeons, caught on the ground. The vultures wings form a 'V' and they rock more than the hawk.
In any case, you can pick out the hawk by her flat wings and steady flight. Or maybe it's just a hawk taking advantage of the vulture's ability to find the best updrafts to ride. It's not clear whether this is a clever strategy to fool prey that would be on the lookout for a hawk but might ignore vultures. They can sometimes be seen among a group of vultures. Red-tailed hawks usually hunt in open areas from a perch on a pole or by soaring in circles over a likely field.