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In a tetrahedron \(ABCD\), we consider the basis \((\Vect{AB}, \Vect{AC}, \Vect{AD})\).
  1. Express the vector \(\Vect{BC}\) in this basis.
  2. Let \(I\) be the midpoint of \([CD]\). Express \(\Vect{AI}\) in this basis.
  3. Give the coordinates of vectors \(\Vect{BC}\) and \(\Vect{AI}\) in the basis \((\Vect{AB}, \Vect{AC}, \Vect{AD})\).

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