\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
The points \(A(1, 1, 1)\), \(B(2, -1, 0)\), and \(C(0, -1, 2)\) are given.
  1. Justify that points \(A, B\), and \(C\) define a plane in space.
  2. Determine a Cartesian equation for the plane \((ABC)\).

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