Forming a query vector in LSA

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After performing the SVD of a term-document matrix, and getting a reduced rank matrix, various sources have stated the following reduced query vector formula. It seems easy to see how its derived.

However, in this link, the query vector is calculated as centroid of the corresponding reduced term vectors. I tried to see if the two were the same, but the results were different.

What is the difference between the two and what are the pros/cons of using either?

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