A particle acted on by constant forces $\vec{F_1} = 4\hat{i} + \hat{j} - 3\hat{k}$ and $\vec{F_2} = 3\hat{i} + \hat{j} - \hat{k}$ is displaced from the point $\vec{d_1} = \hat{i} + 2\hat{j} + 3\hat{k}$ to the point $\vec{d_2} = 5\hat{i} + 4\hat{j} + \hat{k}$. Find the work done.