2) If \(\vec{F} = 2xyz\vec{i} + x^2z\vec{j} + x^2y\vec{k}\), evaluate the integral \(\int \vec{F} \cdot d\vec{r}\) between \(A(0,0,0)\) and \(B(2,4,6)\).
a) Along the curve C whose parametric equations are \(x = u, y = u^2, z = 3u\)
b) Along the three straight lines \(C_1: (0,0,0)\) to \((2,0,0)\); \(C_2: (2,0,0)\) to \((2,4,0)\); \(C_3: (2,4,0)\) to \((2,4,6)\).
c) Determine whether or not \(\vec{F}\) is a conservative field.
