I have two word lists, where each word makes up a topic, and has a tf-idf weight for that topic:

topic1 = [('blue',.1), ('red',.05), ('sky',.01)]
topic2 = [('water',.5), ('fire',.1), ('earth',.02)]

I am trying to calculate the cosine similarity between the vectors, but also account for the tf-idf weighting of each word.

Is there a commonly accepted way to account for individual weightings when doing vector similarity? How would I implement this?