The relevance between Inverted index and Vector Space Model

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These day, I study the Information Retrieval(expecially about Text Retrieval). and I want to make a Search engine. But I confused about the title things that Inverted Index and Vector Space Model(in addition, boolean model etc...for representing document as a vector)

I think Inverted Index is a optional function for Vector Space Model, since this indexing model can help program to get terms(or words) more effectively .... this is my thinking... is right?

please any comment.

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Document-term matrix and inverted index are ways to save documents. After saving the documents you can use vector space model or language models as retrieval models of a search engine.

Also if you just need a search engine made with some data you have and implementing it from the beginning is not your point, you can use Apache Lucene.