A Vector Space is formed from two sets, the vectors and the scalars, which are their coefficients. Vectors form an abelian group with respect to addition, which is to say that sums are closed, associative, commutative, and that there are negatives and a zero.
The scalars comprise a field (supposedly commutative to avoid undue complications, and typically are either the real numbers or, when occasion demands, the complex numbers). That means, among other things, that 1 is a scalar, that scalars have reciprocals, that 0 is also a scalar, and that it is hard to tell the negitive vectors from positive vectors with a negative coefficient.
The distributive laws, right and left, link vector addition with scalar multiplication. Even though there is a right distributive law, coefficients are always written on the left.