spanning over vectors, but this span has only 1 vector

Solution 1:

H spans (and is a basis for) a 1 dimensional subspace of R$^4$.

Solution 2:

Take $R^3$ and cut your span to $span[2, 0, 3]$. Then we have the vector $2, 0, 3$, which spans multiples of $2, 0, 3$ so we have $n(2, 0, 3)$.

Now for $R^4$, do the same. As Betty mentioned it is one-dimensional.

If we had two lines, each with different one-dimensional span, we would end up getting a plane.