Parametrized vectors/abc/Cyclically swapped/Dimensions/Exercise

Let ${}a,b,c\in \mathbb {R}$ be real numbers. We consider the three vectors

${}{\begin{pmatrix}a\\b\\c\end{pmatrix}},\,{\begin{pmatrix}c\\a\\b\end{pmatrix}},\,{\begin{pmatrix}b\\c\\a\end{pmatrix}}\in \mathbb {R} ^{3}\,.$

Give examples for ${}a,b,c$ such that the linear subspace generated by these vectors has dimension ${}0,1,2,3$.

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