\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
In \(\mathbb{R}^4\), set \(a = (0, 0, 1, 0)\), \(b = (1, 1, 0, -1)\), \(u = (1, 0, 1, 0)\), \(v = (0, 1, -1, 0)\), \(w = (1, 1, 1, 1)\), and consider \(F = \mathrm{Vect}(a, b)\) and \(G = \mathrm{Vect}(u, v, w)\). Determine \(F \cap G\).
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