A straight line drawn from the point $P(1,3,2)$, parallel to the line $\frac{x-2}{1}=\frac{y-4}{2}=\frac{z-6}{1}$, intersects the plane $L_1: x-y+3 z=6$ at the point $Q$. Another straight line which passes through $Q$ and is perpendicular to the plane $L_1$ intersects the plane $L_2: 2 x-y+z=-4$ at the point $R$. Then which of the following statements is(are) TRUE?
Select ALL correct options:
A
The length of the line segment PQ is $\sqrt{6}$
B
The coordinates of $R$ are $(1,6,3)$
C
The centroid of the triangle PQR is $\left(\frac{4}{3}, \frac{14}{3}, \frac{5}{3}\right)$
D
The perimeter of the triangle PQR is $\sqrt{2}+\sqrt{6}+\sqrt{11}$
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