\( \definecolor{colordef}{RGB}{249,49,84} \definecolor{colorprop}{RGB}{18,102,241} \)
\(ABCDEFGH\) is a rectangular parallelepiped such that \(AB = 4\), \(AD = 2\), and \(AE = 2\). Let \(I\) be the center of the face \(EFGH\) and \(J\) be the center of the face \(BCGF\).
  1. We consider the orthonormal basis \((A; \Vect{i}, \Vect{j}, \Vect{k})\) such that \(\Vect{AB} = 4\Vect{i}\), \(\Vect{AD} = 2\Vect{j}\), and \(\Vect{AE} = 2\Vect{k}\). Justify that this basis is orthonormal.
  2. Determine the measure of the angle \(\widehat{IAJ}\) in degrees, rounded to the nearest \(0.1^{\circ}\).

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