For some time this summer I have been interning at a university, doing research and working closely with a grad student. The grad student has a very high opinion of me and talks very highly of me to my PI. I think I will continue to return to the lab during the school year to hopefully complete my project and publish a paper on the work I have done.
The question is this: should I ask for a recommendation letter from the PI? The professor is very nice to me and I have spoken to him on several occasions, but he is a very hands off PI as his lab is very large so he is not aware of how I am in the lab or what exactly it is that I do, other than what he has heard from the grad student. Basically he knows that I am smart, but doesn’t know me very personally. I could also ask the grad student for a letter, but I don’t really know if I am allowed to.
In short, would the PI’s letter add anything to my application at all, if he does not work with me directly?
Some additional information: I also wanted to ask for an additional recommendation letter from my art teacher, as art has been a very large part of my high school career and I don’t believe my academic recommenders could speak to that.
I would appreciate any advice!