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?
Select ALL correct options:
A
(A) The length of the line segment $P Q$ is $9 \sqrt{3}$
B
The length of the line segment $Q R$ is 15
C
The area of $\triangle P Q R$ is $\frac{3}{2} \sqrt{234}$
D
The acute angle between the line segments $P Q$ and $P R$ is $\cos ^{-1}\left(\frac{1}{2 \sqrt{3}}\right)$
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