Two point charges of $100\,\mu\text{C}$ and $-4\,\mu\text{C}$ are positioned at points $(-2\sqrt{3}, 3\sqrt{3}, -4)$ and $(4\sqrt{3}, -5\sqrt{3}, 6)$ respectively of a Cartesian coordinate system. Find the force vector on the $-4\,\mu\text{C}$ charge. All the coordinates are in meters.