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