1-In a vector model, how would you define the proximity between two documents? Propose a measure that takes into account the frequency of terms and the inverse frequency of terms, and that does not favor longer documents.

2-Precision and recall are very common measures in information retrieval. Specify the limits of these measures in a distributed context such as the web.

3-Vector models generally do not take into account language-specific features, such as synonymy. Explain how Latent Semantic Indexing can be a solution to this type of problem and thus contribute to improving the quality of the results.