In an orthonormal coordinate system of space, we consider the following points:
$$\mathrm{A}(2;-1;0),\quad \mathrm{B}(3;-1;2),\quad \mathrm{C}(0;4;1)\quad \text{and}\quad \mathrm{S}(0;1;4).$$

\begin{enumerate}
  \item Show that triangle ABC is right-angled at A.
  \item a. Show that the vector $\vec{n}\begin{pmatrix}2\\1\\-1\end{pmatrix}$ is orthogonal to the plane (ABC).\\
  b. Deduce a Cartesian equation of the plane (ABC).\\
  c. Show that the points A, B, C and S are not coplanar.
  \item Let (d) be the line perpendicular to the plane (ABC) passing through S. It intersects the plane (ABC) at H.\\
  a. Determine a parametric representation of the line (d).\\
  b. Show that the coordinates of point H are $\mathrm{H}(2;2;3)$.
  \item We recall that the volume $V$ of a tetrahedron is $V = \dfrac{\text{area of base} \times \text{height}}{3}$. Calculate the volume of tetrahedron SABC.
  \item a. Calculate the length SA.\\
  b. We are told that $\mathrm{SB} = \sqrt{17}$. Deduce an approximate measure of the angle $\widehat{\mathrm{ASB}}$ to the nearest tenth of a degree.
\end{enumerate}