An electric dipole is placed within an electric field produced by a...

The electric field produced by a point charge is non-uniform, as its magnitude varies with distance and its direction is radial.

Since the two charges of the dipole are at different positions, they will experience different electric fields ($\vec{E}_1 \neq \vec{E}_2$).

The net force on the dipole is $\vec{F}_{net} = q\vec{E}_1 - q\vec{E}_2 \neq 0$. Thus, the net electric force can never be zero.

The torque on the dipole is given by $\vec{\tau} = \vec{p} \times \vec{E}$.

If the dipole is placed such that its dipole moment $\vec{p}$ is parallel or anti-parallel to the electric field $\vec{E}$ (i.e., oriented along the radial line from the point charge), the angle between them is $0^{{}^{{}^{\circ}}}$ or $180^{{}^{{}^{\circ}}}$.

In this case, the torque $\vec{\tau} = 0$. Therefore, the torque on the dipole could be zero.