Given two vectors; \( \overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+\hat{\mathbf{j}} \) and \( \o....

Given two vectors; \( \overrightarrow{\mathbf{A}}=\hat{\mathbf{i}}+\hat{\mathbf{j}} \) and \( \overrightarrow{\mathbf{B}}=\hat{\mathbf{i}}-\hat{\mathbf{j}} \). Then
\( \mathrm{P} \)
match the following columns :
\begin{tabular}{|l|l|l|l|}
\hline & \multicolumn{1}{|c|}{ Column I } & & Column II \\
\hline\( (\mathrm{A}) \) & \( (\overrightarrow{\mathbf{A}}+\overrightarrow{\mathbf{B}}) / 2 \) & \( (\mathrm{p}) \) & \( \hat{\mathbf{i}} \) \\
\hline (B) & \( (\overrightarrow{\mathbf{A}}-\overrightarrow{\mathbf{B}}) / 2 \) & \( (\mathrm{q}) \) & \( \hat{\mathbf{j}} \) \\
\hline\( (\mathrm{C}) \) & \( (\overrightarrow{\mathbf{A}} \cdot \overrightarrow{\mathbf{B}}) / 2 \) & \( (\mathrm{r}) \) & \( \hat{\mathbf{k}} \) \\
\hline (D) & \( (\overrightarrow{\mathbf{A}} \times \overrightarrow{\mathbf{B}}) / 2 \) & \( (\mathrm{~s}) \) & \( -\hat{\mathbf{k}} \) \\
\hline & & (t) & zero \\
\hline
\end{tabular}
(1) \( \mathrm{A} \rightarrow \mathrm{q} ; \mathrm{B} \rightarrow \mathrm{p} ; \mathrm{C} \rightarrow \mathrm{r} ; \mathrm{D} \rightarrow \mathrm{s} \)
(2) \( \mathrm{A} \rightarrow \mathrm{p} ; \mathrm{B} \rightarrow \mathrm{q} ; \mathrm{C} \rightarrow \mathrm{t} ; \mathrm{D} \rightarrow \mathrm{s} \)
(3) \( \mathrm{A} \rightarrow \mathrm{p} ; \mathrm{B} \rightarrow \mathrm{q} ; \mathrm{C} \rightarrow \mathrm{r} ; \mathrm{D} \rightarrow \mathrm{s} \)
(4) \( \mathrm{A} \rightarrow \mathrm{t} ; \mathrm{B} \rightarrow \mathrm{q} ; \mathrm{C} \rightarrow \mathrm{p} ; \mathrm{D} \rightarrow \mathrm{r} \)