Question Match of the following lists: \begin{tabular}{|c|c|c|c|} \hline & List-I & & List-II \\....
0Question Match of the following lists:
\begin{tabular}{|c|c|c|c|}
\hline & List-I & & List-II \\
\hline (A) & \begin{tabular}{l}
If \( |\vec{a}|=|\vec{b}|=|\vec{c}| \), angle between each \\
pair of vectors is \( \frac{\pi}{3} \) and \\
\( |\vec{a}+\vec{b}+\vec{c}|=\sqrt{6} \), then \( 2|\vec{a}| \) is equal to
\end{tabular} & (P) & 3 \\
\hline (B) & \begin{tabular}{l}
If \( \vec{a} \) is perpendicular to \( \vec{b}+\vec{c}, \vec{b} \) is \\
perpendicular to \( \vec{c}+\vec{a}, \vec{c} \) is \\
perpendicular \( \vec{a}+\vec{b},|\vec{a}|=2,|\vec{b}|=3 \) \\
and \( |\vec{c}|=6 \), then \( |\vec{a}+\vec{b}+\vec{c}|-2 \) is \\
equal to
\end{tabular} & (Q) & 2 \\
\hline (C) & \begin{tabular}{l}
\( \vec{a}=2 \hat{i}+3 \hat{j}-\hat{k}, \quad \vec{b}=-\hat{i}+2 \hat{j}-4 \hat{k} \), \\
\( \vec{c}=\hat{i}+\hat{j}+\hat{k} \) and \( \vec{d}=3 \hat{i}+2 \hat{j}+\hat{k} \), \\
then \( \frac{1}{7}(\vec{a} \times \vec{b}) \cdot(\vec{c} \times \vec{d}) \) is equal to
\end{tabular} & (R) & 4 \\
\hline (D) & \begin{tabular}{l}
If \( \quad|\vec{a}|=|\vec{b}|=|\vec{c}|=2 \) \\
\( \vec{a} \cdot \vec{b}=\vec{b} \cdot \vec{c}=\vec{c} \cdot \vec{a}=2 \), and \\
{\( [\vec{a} \vec{b} \vec{c}] \cos 45^{\circ} \) is equal to }
\end{tabular} & (S) & 5 \\
\hline
\end{tabular}
Codes:
\begin{tabular}{lllll}
& A & B & C & D \\
(1) & \( \mathrm{P} \) & \( \mathrm{Q} \) & \( \mathrm{R} \) & \( \mathrm{S} \) \\
(2) & \( \mathrm{S} \) & \( \mathrm{R} \) & \( \mathrm{Q} \) & \( \mathrm{P} \) \\
(3) & \( \mathrm{Q} \) & \( \mathrm{S} \) & \( \mathrm{P} \) & \( \mathrm{R} \) \\
(4) & \( \mathrm{R} \) & \( \mathrm{P} \) & \( \mathrm{S} \) & \( \mathrm{Q} \)
\end{tabular}
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