Need help with determining subspaces! (1st year Lin. Alg.)

The question is: For each of the following subsets of S of R^5, determine if S is a subspace. Explain and prove your choice by using the three properties. a) S the set of all vectors with all entries rational numbers. b) S = {v is an element of R^5 | v . (4, -1007, 0, -1, 356) = 0}. c) S = {v is an element of R^5 | v.v is greater than or equal to 0}.

My thinking, can you please verify these? a) If v is a vector of R^5 and an element of S, when multiplied by a scalar (say 10) then the result would be closed under scalar multiplication as the resulting set of entries are rational numbers. However, if the scalar was multiplied by an irrational number (say pi), then the resulting set would also be irrational, thus not being an element of S and not being closed under scalar multiplication. b) I think this set is a subspace of S, but I am not quite sure how to prove it as I have never seen a question written in that way. c) I don't think this subspace is a subset of S, as it will not be closed under scalar multiplication. For example, (1,0) is an element of S, however (-1)(1,0) = (-1,0), which is not an element of S.

Thanks! :)