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Many Formulations could be possible. I am writing one of the possible SQL expressions for the above Query.

The Resultant Vector (U + V) will be corresponding to the following Table in SQL : 

SELECT  ind, SUM(val)

FROM  (  SELECT ind,val

                  FROM U

                 UNION ALL

                 SELECT ind,val

                 FROM V             )

GROUP BY  ind

ORDER BY  ind     ;

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