5.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{1be33445-e669-49af-a97e-a8ae84d63463-12_762_1129_246_468}
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\caption{Figure 1}
\end{figure}
The points \(A ( 3,2 , - 4 ) , B ( 9 , - 4,2 ) , C ( - 6 , - 10,8 )\) and \(D ( - 4 , - 5,10 )\) are the vertices of a tetrahedron.
The plane with equation \(z = 0\) cuts the tetrahedron into two pieces, one on each side of the plane.
The edges \(A B , A C\) and \(A D\) of the tetrahedron intersect the plane at the points \(M , N\) and \(P\) respectively, as shown in Figure 1.
Determine
- the coordinates of the points \(M , N\) and \(P\),
- the area of triangle \(M N P\),
- the exact volume of the solid \(B C D P N M\).