Let $\vec { w } = \hat { \imath } + \hat { \jmath } - 2 \hat { k }$, and $\vec { u }$ and $\vec { v }$ be two vectors, such that $\vec { u } \times \vec { v } = \vec { w }$ and $\vec { v } \times \vec { w } = \vec { u }$. Let $\alpha , \beta , \gamma$, and $t$ be real numbers such that
$\vec { u } = \alpha \hat { \imath } + \beta \hat { \jmath } + \gamma \hat { k } , \quad - t \alpha + \beta + \gamma = 0 , \quad \alpha - t \beta + \gamma = 0 , \quad$ and $\alpha + \beta - t \gamma = 0$.

Match each entry in List-I to the correct entry in List-II and choose the correct option.

\section*{List-I}
(P) $| \vec { v } | ^ { 2 }$ is equal to\\
(Q) If $\alpha = \sqrt { 3 }$, then $\gamma ^ { 2 }$ is equal to\\
(R) If $\alpha = \sqrt { 3 }$, then $( \beta + \gamma ) ^ { 2 }$ is equal to\\
(S) If $\alpha = \sqrt { 2 }$, then $t + 3$ is equal to

\section*{List-II}
(1) 0\\
(2) 1\\
(3) 2\\
(4) 3\\
(5) 5

\begin{center}
\begin{tabular}{|l|l|l|l|l|}
\hline
(A) & $( \mathrm { P } ) \rightarrow ( 2 )$ & $( \mathrm { Q } ) \rightarrow ( 1 )$ & $( \mathrm { R } ) \rightarrow ( 4 )$ & $( \mathrm { S } ) \rightarrow ( 5 )$ \\
\hline
(B) & $( \mathrm { P } ) \rightarrow ( 2 )$ & $( \mathrm { Q } ) \rightarrow ( 4 )$ & $( \mathrm { R } ) \rightarrow ( 3 )$ & $( \mathrm { S } ) \rightarrow ( 5 )$ \\
\hline
(C) & $( \mathrm { P } ) \rightarrow ( 2 )$ & $( \mathrm { Q } ) \rightarrow ( 1 )$ & $( \mathrm { R } ) \rightarrow ( 4 )$ & $( \mathrm { S } ) \rightarrow ( 3 )$ \\
\hline
(D) & $( \mathrm { P } ) \rightarrow ( 5 )$ & $( \mathrm { Q } ) \rightarrow ( 4 )$ & $( \mathrm { R } ) \rightarrow ( 1 )$ & $( \mathrm { S } ) \rightarrow ( 3 )$ \\
\hline
\end{tabular}
\end{center}