Let $L _ { 1 }$ be the line of intersection of the planes given by the equations

$$2 x + 3 y + z = 4 \text { and } x + 2 y + z = 5 .$$

Let $L _ { 2 }$ be the line passing through the point $P ( 2 , - 1,3 )$ and parallel to $L _ { 1 }$. Let $M$ denote the plane given by the equation

$$2 x + y - 2 z = 6$$

Suppose that the line $L _ { 2 }$ meets the plane $M$ at the point $Q$. Let $R$ be the foot of the perpendicular drawn from $P$ to the plane $M$.

Then which of the following statements is (are) TRUE?

\begin{center}
\begin{tabular}{|l|l|}
\hline
(A) & The length of the line segment $PQ$ is $9 \sqrt { 3 }$ \\
\hline
(B) & The length of the line segment $QR$ is 15 \\
\hline
(C) & The area of $\triangle PQR$ is $\frac { 3 } { 2 } \sqrt { 234 }$ \\
\hline
(D) & The acute angle between the line segments $PQ$ and $PR$ is $\cos ^ { - 1 } \left( \frac { 1 } { 2 \sqrt { 3 } } \right)$ \\
\hline
\end{tabular}
\end{center}