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In space, consider the line \(d\) passing through \(E(1, 1, 1)\) with direction vector \(\Vect{w}(1, 1, 1)\) and the plane \(\mathscr{P}\) defined by the direction vectors \(\Vect{u}(1, 0, 1)\) and \(\Vect{v}(0, 1, -1)\). Show that the line \(d\) is not parallel to the plane \(\mathscr{P}\).
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