In the vector model, a query Q is represented as an attribute vector in a
similar fashion to documents:
where 
represents the weight of attribute 
in Q.
In order to determine which documents satisfy the query, some
similarity measure, or document ranking function, r is
needed. Common values for r are the simple dot product
the cosine function
and the similarity function
Of note is that when the entries of Q and d are restricted to either 0 or 1, the dot product returns the number of terms contained in both Q and d. The denominators of r'' and r''' are two different methods to normalize for document length.
In order to satisfy a given query Q, r(Q, d) is computed
for all 
, and those documents with sufficiently high values
of r are returned, usually in sorted order of decreasing value or in some
kind of clustered display [54].