\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}^3\), find a necessary and sufficient condition on \(a \in \mathbb{R}\) for the vector \((1, -a, 1)\) to be a linear combination of \((1, 1, 1)\) and \((a, 0, 2)\).
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