Prove that span(x) = ax : a in ℝ for any vector x in a vector space. Interpret this result geometrically in ℝ³.
a) The span of a single vector is all scalar multiples of that vector.
b) The span of a single vector is always zero.
c) The span of a single vector is always a line passing through the origin.
d) The span of a single vector is always a plane passing through the origin.