Let a line passing through the point $(-1, 2, 3)$ intersect the lines $L_1: \frac{x-1}{3} = \frac{y-2}{2} = \frac{z+1}{-2}$ at $M(\alpha, \beta, \gamma)$ and $L_2: \frac{x+2}{-3} = \frac{y-2}{-2} = \frac{z-1}{4}$ at $N(a, b, c)$. Then the value of $\frac{(\alpha + \beta + \gamma)^2}{(a + b + c)^2}$ equals $\underline{\hspace{1cm}}$.

A unit cube $ABCD-EFGH$ with edge length 1. Point $P$ is the midpoint of edge $\overline{CG}$. Points $Q$ and $R$ are on edges $\overline{BF}$ and $\overline{DH}$ respectively, and $A$, $Q$, $P$, $R$ are the four vertices of a parallelogram, as shown in the figure below.
A coordinate system is established such that the coordinates of $D$, $A$, $C$, $H$ are $(0, 0, 0)$, $(1, 0, 0)$, $(0, 1, 0)$, $(0, 0, 1)$ respectively, and $\overline{BQ} = t$. Answer the following questions.
(1) Find the coordinates of point $P$. (2 points)
(2) Find the vector $\overrightarrow{AR}$ (express in terms of $t$). (2 points)
(3) Prove that the volume of the pyramid $G-AQPR$ is a constant (independent of $t$), and find this constant value. (4 points)
(4) When $t = \frac{1}{4}$, find the distance from point $G$ to the plane containing parallelogram $AQPR$. (4 points)

In space, there is a unit cube with edge length 1. Point $O$ is one vertex, and the remaining 7 vertices are $A, B, C, D, E, F, G$. Given that $\overline { O A } = \overline { A B } = \overline { B C } = \overline { C D } = \overline { D E } = \overline { E F } = \overline { F G } = 1$ and $\overline { O G } > 1$, select the vertex farthest from point $O$.
(1) $C$
(2) $D$
(3) $E$
(4) $F$
(5) $G$