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.
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R3 is a complete vector room, so you can actually take *ANY* other vector, e.g. from r1, r2 or r4 or any other vector room.
When b is zero.
It is the rate of change in the vector for a unit change in the direction under consideration. It may be calculated as the derivative of the vector in the relevant direction.
if the vector is oriented at 45 degrees from the axes.
if b + a , since a+b equals b + a due to it being commutative . it shud have the same magnitude and direction