The system can be treated as the superposition of two electric dipoles. The charge -2q at the origin (0,0,0) can be split into two charges of -q.

1. Dipole 1: Formed by -q at (0,0,0) and +q at (a,0,0). The dipole moment vector $\vec{p}_1$ points from negative to positive charge, i.e., along the +x axis. Magnitude $p_1 = q \times a$. So, $\vec{p}_1 = qa \hat{i}$.
2. Dipole 2: Formed by the remaining -q at (0,0,0) and +q at (0,a,0). The dipole moment vector $\vec{p}_2$ points along the +y axis. Magnitude $p_2 = q \times a$. So, $\vec{p}_2 = qa \hat{j}$.
3. Resultant Dipole Moment: $\vec{p}_{net} = \vec{p}_1 + \vec{p}_2 = qa(\hat{i} + \hat{j})$.
4. Magnitude: $|\vec{p}_{net}| = \sqrt{(qa)^2 + (qa)^2} = \sqrt{2}qa$.
5. Direction: The vector $\hat{i} + \hat{j}$ lies in the xy-plane at 45° to the x-axis, which corresponds to the line joining the origin (0,0,0) and the point (a,a,0).