\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
Let \(F = \{(x, y, z) \in \mathbb{R}^3 : x + y + z = 0\}\). Show that \(G = \mathrm{Vect}\bigl((1, 0, 0)\bigr)\) is a supplement of \(F\) in \(\mathbb{R}^3\).
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