According to the definition of work done by a constant force, work ($W$) is the scalar product of the force vector ($\mathbf{F}$) and the displacement vector ($\mathbf{d}$), expressed as $W = \mathbf{F} \cdot \mathbf{d}$ .

1. Find the displacement vector ($\mathbf{d}$): Displacement is the difference between the final position ($\mathbf{r_2}$) and the initial position ($\mathbf{r_1}$) . $\mathbf{d} = \mathbf{r_2} - \mathbf{r_1} = (4\hat{i} + 3\hat{j} - \hat{k}) - (2\hat{i} + \hat{k})$ $\mathbf{d} = (4-2)\hat{i} + (3-0)\hat{j} + (-1-1)\hat{k} = 2\hat{i} + 3\hat{j} - 2\hat{k} \text{ m}$

2. Calculate the scalar product: Multiply the corresponding components of the force $\mathbf{F} = (3\hat{i} + \hat{j} + 0\hat{k})$ N and the displacement vector . $W = (3)(2) + (1)(3) + (0)(-2)$ $W = 6 + 3 + 0 = 9 \text{ J}$

Thus, the work done by the force is 9 J.