Find the gradient field of the function g(x,y,z) = 6xy + yz + Xz. Vg= (Type your answer in terms of i, j, and k.)Find the line integral of F = \\zi- 2xj + 2 vyk, from (0,0,0) to (1, 1,1) over each of the following paths. a. The straight-line path C, : r(t) = ti + tj + tk, Osts 1 (0, 0, 0) (1, 1, 1) b. The curved path C2: r(t) = ti + tej+ t*k, Osts1 c. The path C3 UC4 consisting of the line segment from (0,0,0) to (1, 1,0) followed by the segment from (1, 1,0) to (1, 1, 1) a. The line integral of F over the straight-line path C, is]. (Type an integer or a simplified fraction.) b. The line integral of F over the curved path C2 is. (Type an integer or a simplified fraction.) c. The line integral of F over the path CUC4 is]. (Type an integer or a simplified fraction.)