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There does not seem to be an under vector room, but there is vector space. Vector space is a structure that is formed by a collection of vectors. This is a term in mathematics.
Vector spaces can be formed of vector subspaces.
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You need to know that the cross product of two vectors is a vector perpendicular to both vectors. It is defined only in 3 space. The formula to find the cross product of vector a (vector a=[a1,a2,a3]) and vector b (vector b=[b1,b2,b3]) is: vector a x vector b = [a2b3-a3b2,a3b1-a1b3,a1b2-a2b1]
Comparison of space vector modulation techniques based onperformance indexes and hardware implementation