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\(ABCD\) is a parallelogram. Consider the basis \((\Vect{AB}, \Vect{AD})\) with origin \(A\).
  1. Express \(\Vect{AC}\) in terms of \(\Vect{AB}\) and \(\Vect{AD}\).
  2. Let \(I\) be the center of the parallelogram. Express \(\Vect{AI}\) in the basis \((\Vect{AB}, \Vect{AD})\).
  3. Give the coordinates of \(\Vect{BD}\) and \(\Vect{AI}\) in this basis.

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