Is there a subspace of $R^3$ of dimension $1$ that contains the vectors $v=(1,1,2)$ and $w=(1,-1,2)$? 
Is there a subspace of $R^3$ of dimension $1$ that contains the vectors $v=(1,1,2)$ and $w=(1,-1,2)$?

I see that $v$ and $w$ linearly independent so I think that there isn't a subspace of dimension $1$ that contains both vectors. But I think that there is a subspace of dimension 2 that contains $v$ and $w$.
My question is whether my reasoning is correct and how to justify it.

Please note that $$\det
    \begin{vmatrix}
    1 & 2 \\
    -1 & 2\\
    \end{vmatrix}=4
$$ so the vectors mentioned are linearly independant. That means that they produce a subspace of $\mathbb{R}^3$ of dimension $2$.
