Motivation When you want to find some information by using Search Engines, you have to make a query used for search. Unfortunately, since you don't know exactly what it means, your query will be ambiguous and not accurate. Therefore, Search Engines give you the information in a ranked list rather than the right position. Intuition In order to make a ranked list, you need to calculate the similarity between the query and documents based on terms or words. One of the calculation of similarity is dot product on a vector space. In the vector space, there are many documents with respect to word dimensions The first to rank is d2, because to see with eyes it's the most similarity with the query. Problem How do we plot those vectors wonderfully and nicely and very very fairly ? - How do we define the dimension ? - How do we place a document vector ? - How do we place a query vector ? - How do we match a similarity ? Consideration 1. The frequency of each word of Query. First, Score in