Please show all work. Thank you!

Consider the vector field F = (1622, 6sec2(y), 32xz) . Be sure to include all of your work for this problem. No work means no credit. (a) Determine the curl of this vector field. V X F = ( 0 (b) Which of the following are true about F? (Select all that apply.) OF is a rotation vector field OF is a gradient field OF is a divergent field O F is orthogonal OF is irrotational OF is conservative OF is source free OF has a potential function O Any line integral in F is path independent O Any line integral in F is path dependent O All of the above. O None of the above. (c) Determine the potential function for F. If it does not have a potential function, then enter DNE. A( x , y , 2 ) = + K (d) Determine the circulation of F around the curve given by the intersection of the cone = 4 and the sphere p = 1 . Evaluate any integrals by hand or explain any properties or theorems used to justify your