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?