1. **State the problem:** We are given two electric charges Q₁ and Q₂ located at points with Cartesian coordinates (1, 2, 3) and (−1, −3, 3) respectively. We need to determine: (I) The distance vector $\overrightarrow{Q_1 Q_2}$ (II) The distance between Q₁ and Q₂. 2. **Formula and rules:** - The distance vector from point $Q_1(x_1,y_1,z_1)$ to $Q_2(x_2,y_2,z_2)$ is given by: $$\overrightarrow{Q_1 Q_2} = (x_2 - x_1, y_2 - y_1, z_2 - z_1)$$ - The distance between two points in 3D space is the magnitude of the distance vector: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}$$ 3. **Calculate the distance vector:** Given $Q_1 = (1, 2, 3)$ and $Q_2 = (-1, -3, 3)$, $$\overrightarrow{Q_1 Q_2} = (-1 - 1, -3 - 2, 3 - 3) = (-2, -5, 0)$$ 4. **Calculate the distance:** $$d = \sqrt{(-2)^2 + (-5)^2 + 0^2} = \sqrt{4 + 25 + 0} = \sqrt{29}$$ 5. **Final answers:** (I) Distance vector $\overrightarrow{Q_1 Q_2} = (-2, -5, 0)$ (II) Distance between Q₁ and Q₂ is $\sqrt{29}$ units.