A groove is in the form of a broken line ABC and the position vectors of the three points are, respectively, $ \vec{A} = 2\hat{i} - 3\hat{j} + 2\hat{k} $, $ \vec{B} = 3\hat{i} - \hat{k} $, and $ \vec{C} = \hat{i} + \hat{j} + \hat{k} $. A force of magnitude $24\sqrt{3}$ acts on a particle of unit mass kept at point A and moves it along the groove to point C. If the line of action of the force is parallel to the vector $ \hat{i} + 2\hat{j} + \hat{k} $ all along, the number of units of work done by the force is: