If c is the curve given by \mathbf{r} \left( t \right = \left( 1 5 \sin t \right \mathbf{i} \left( 1 3 \sin^{2} t \right \mathbf{j} \left( 1 2 \sin^{3} t \right \mathbf{k}, 0 \leq t \leq \frac{\pi}{2} and f is the radial vector field \mathbf{f} \left( x, y, z \right = x \mathbf{i} y \mathbf{j} z \mathbf{k}, compute the work done by f on a particle moving along c