Teaching CSIR NET Mock Test Series Mathematical Science

Let V be the span of (1, 1, 1) and (0, 1, 1) ∈ ℝ3. Let u1 = (0, 0, 1), u2 = (1, 1, 0) and u3 = (1, 0, 1). Which of the following are correct?

1
(ℝ3\V) ∪ {(0, 0, 0)} is not connected
2
(ℝ3\V) ∪ {tu1 + (1 - t)u3: 0 ≤ t ≤ 1} is connected
3
(ℝ3\V) ∪ {tu1 + (1 - t)u2: 0 ≤ t ≤ 1} is connected
4
(ℝ3\V) ∪ {(t, 2t, 2t): t ∈ ℝ} is connected
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