A couple of answers point out that this question has no correct answer for an arbitrary vector. Just as in ordinary multiplication, division by 0.5 is the same and multiplication by 2, and vice versa.
However, if you interpret the question as implying a guarantee that one of those answers is indeed correct, then you get an interesting conclusion: The only way for one of those answers to be correct for all x>0 is for the vector to be the zero vector!
Division of a vector by a real number is defined as multiplication of the vector by the reciprocal of that real number. Multiplying the zero vector by any number gives the zero vector as a product. So, if I had to pick an answer to this question, I'd choose "(c) it remains the same".
That sort of "trick question" thinking is probably better left to solving "brain teaser" type puzzles. In a serious math course, the conditions ought to be clearly spelled out.