Consider the following scalar and vector functions and answerthe following question:

o(x, y, z) = xy + xyz. = yzi + 4xyj + yk. F = v + _=_=ln(y)] + yk. (a) Find the gradient of the scalar field, o denoted as Vo. Evaluate the gradient at point (2,1,0) and find the magnitude. (b) Find the divergence of the vector, F. When the divergence equal to zero in the z 0, y = 3 plane? (c) Find the curl of the vector, . (d) Determine the following if they are valid: i. V x V x ii. (V x E). Vo iii. (V x F).(V x o) iv. V(V.) v. (V x E) x (V.F)