Consider the points \(A(1, 0, 2)\), \(B(3, 1, 4)\) and \(C(0, 5, 3)\).

(a) Find the vector \(\vec{AB}\) and the vector \(\vec{AC}\). [2]
(b) Find the vector product \(\vec{AB} \times \vec{AC}\). [3]
(c) Hence, find the area of triangle \(ABC\). [2]
(d) Find the Cartesian equation of the plane \(\Pi\) containing the points A, B and C. [3]

The line \(L\) has vector equation \(\mathbf{r} = (2, -1, 0) + t(1, -2, 1)\), where \(t \in \mathbb{R}\).
(e) Show that the line \(L\) intersects the plane \(\Pi\). [4]
(f) Find the coordinates of the point of intersection \(P\) of the line \(L\) and the plane \(\Pi\). [3]
(g) Find the angle between the line \(L\) and the plane \(\Pi\). [2]