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In space, consider the following points:$$ A(1, 2, 1), \quad B(3, 4, 1), \quad C(2, 2, 0), \quad \text{and} \quad D(2, 4, 2) $$
  1. Determine the coordinates of the direction vectors \(\Vect{AB}\) and \(\Vect{CD}\).
  2. Justify that the lines \((AB)\) and \((CD)\) are not parallel.
  3. Give a parametric representation for each of the lines \((AB)\) and \((CD)\).
  4. By solving a system, show that the lines \((AB)\) and \((CD)\) are secant and determine the coordinates of their intersection point \(I\).

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