Solution:

Given:
- Dipole moment: \( \overrightarrow{p} = 3\hat{i} + 4\hat{j} \) C·m
- Electric field: \( \overrightarrow{E} = 0.4 \, \text{kN/C} \hat{i} = 400 \, \text{N/C} \hat{i} \)

Torque (\( \overrightarrow{\tau} \)):
\[
\overrightarrow{\tau} = \overrightarrow{p} \times \overrightarrow{E}
\]

\[
\overrightarrow{\tau} = \begin{vmatrix}
\hat{i} & \hat{j} & \hat{k} \\
3 & 4 & 0 \\
400 & 0 & 0
\end{vmatrix} = \hat{k} \big(3(0) - 4(400)\big) = -1600\hat{k} \, \text{N·m}
\]

Potential Energy (\( U \)):
\[
U = -\overrightarrow{p} \cdot \overrightarrow{E}
\]
\[
U = -(3 \times 400 + 4 \times 0) = -1200 \, \text{J}
\]

Final Answer:
- Torque: \( -1600 \, \text{N·m} \hat{k} \)
- Potential energy: \( -1200 \, \text{J} \)