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Suppose \(\Vect{a}=\begin{pmatrix}1 \\ 2 \\ 3\end{pmatrix}\) and \(\Vect{b}=\begin{pmatrix}-1 \\ 3 \\ -1\end{pmatrix}\).
  1. Find \(\Vect{a} \times \Vect{b}\).
  2. Hence determine \(\Vect{a} \cdot (\Vect{a} \times \Vect{b})\) and \(\Vect{b} \cdot(\Vect{a} \times \Vect{b})\).
  3. Explain your results.

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