\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}^3\), set \(F = \{(x, y, z) \in \mathbb{R}^3 : x + y + z = 0\}\) and \(G = \mathrm{Vect}\bigl((1, 1, 1)\bigr)\). Show that \(F\) and \(G\) are in direct sum.
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