For each of the following propositions, indicate whether it is true or false and justify each answer. An unjustified answer will not be taken into account.

We are in space with an orthonormal coordinate system.\\
We consider the plane $\mathscr{P}$ with equation $x - y + 3z + 1 = 0$\\
and the line $\mathscr{D}$ whose parametric representation is\\
$\left\{\begin{array}{l} x = 2t \\ y = 1 + t \\ z = -5 + 3t \end{array}, \quad t \in \mathbb{R}\right.$\\
We are given the points $A(1; 1; 0)$, $B(3; 0; -1)$ and $C(7; 1; -2)$

\textbf{Proposition 1:}\\
A parametric representation of the line $(AB)$ is $\left\{\begin{array}{l} x = 5 - 2t \\ y = -1 + t \\ z = -2 + t \end{array}, t \in \mathbb{R}\right.$

\textbf{Proposition 2:}\\
The lines $\mathscr{D}$ and $(AB)$ are orthogonal.

\textbf{Proposition 3:}\\
The lines $\mathscr{D}$ and $(AB)$ are coplanar.

\textbf{Proposition 4:}\\
The line $\mathscr{D}$ intersects the plane $\mathscr{P}$ at point $E$ with coordinates $(8; -3; -4)$.

\textbf{Proposition 5:}\\
The planes $\mathscr{P}$ and $(ABC)$ are parallel.