please give answer to the following calculus question with step by step calculation to understand clearly

5. (a) [3 marks] Show that the vector field F = (12x2y + 6%2, 4:3 -- 20yz, 12:z - 10g2) is irrotational that is V x F = 0. (b) [4 marks] Find a potential function for F. (c) [2 marks] Evaluate the work integral f, F . dr, where C is a path running from the origin to the point (1,2, 1). * f i N