Your vanity light should be about 75 percent of the vanity. In this case, the vanity light would need to be around 27 inches long. This length allows you to get ample illumination for the vanity while also not overcrowding the space.
For a 9-ft island, it is generally recommended that you choose between two or three pendant fixtures. Adding more lights may lead to too much light which can lead to discomfort. While only using one light may lead to less light and a need for more lighting. However, the actual number of lights you choose might vary based on personal preference.