For example, could the vectors $(0, 1, 2)$ and $(1, 0, 2)$ potentially span $\mathbb{R}^2$ and be linearly independent?

I've seen a bunch of articles that say two vectors cannot span $\mathbb{R}^3$ which makes sense to me, but it seems to me that if the last coordinates of the vectors were $0$ then they could span a plane.

I know that normally a candidate basis is disqualified if it has more vectors than needed, but in this case the vector would have more entries than needed so I am not sure if that still holds.

I am asking for my homework as I'm pretty confused.