A groove is in the form of a broken line ABC and the position vectors of the three points are respectively $2\hat i - 3\hat j + 2\hat k, 3\hat i +2\hat j-\hat k,\hat i+\hat j+\hat k$. A force of magnitude $24\sqrt{3}$ acts on a particle of unit mass kept at the point A and moves it along the groove to the 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 

$72\sqrt{2}$

Work done = $\vec F. (\vec{AB} + \vec{BC}) = \vec F.\vec{AC}$

we have,

$\vec F=\frac{24\sqrt{3}(\hat i+2\hat j+\hat k)}{\sqrt{6}}=12\sqrt{2}(\hat i+2\hat j+\hat k)$

and $\vec{AC}=-\hat i+4\hat j-\hat k$

∴ Work done = $\vec F.\vec{AC}=72\sqrt{2}$