(Solved): 6. If \( \mathbf{F}=y^{2} \mathbf{i}+2 x \mathbf{j}+4 z \mathbf{k} \), evaluate \( \int_{(0,0,0)}^ ...

6. If \( \mathbf{F}=y^{2} \mathbf{i}+2 x \mathbf{j}+4 z \mathbf{k} \), evaluate \( \int_{(0,0,0)}^{(1,1,1)} \mathbf{F} \cdot d \mathbf{r} \) along the paths: a. The rectilinear path from \( (0,0,0) \) to \( (1,0,0) \) to \( (1,1,0) \) to \( (1,1,1) \) b. The straight line from \( (0,0,0) \) to \( (1,1,1) \)