If what you want is a quotation or offer, then sending a letter of intent makes you look ignorant while requesting a quotation will generally at least make you look like you know what it is that you want. And what you want, after all, is a price quote. Hence you want to request a price quote, via a request for quotation.
Letters of intent can be used in situations where a group of students wish to organize a specific club or perhaps a new fraternity. In the letter they can state their reasons for taking this action, how many members they expect to have and what they think they are going to accomplish. The letter can also outline the requirements for membership and in many cases the basic rules of behavior that will be expected for continued membership. Students might also write a skillfully prepared letter to the admissions office of the college they wish to attend and include it with the rest of their application package.