ways to represent document by its keyword vectors
If you have the vectors for your keywords, you can aggregate those to get the document vectors. The simplest(and probably one of the most effective) way is to average out your keyword vectors to form the document vector. Once you have the vectors for each of the documents, you can use similarity measures like cosine similarity to see how close your documents are. 
A typical example of such a method is this :


Edit: Another interesting point would be to evaluate how you are getting your word vectors. Please look at pretrained word embeddings like word2vec, Glove or Fast Text.