i. A field occupies space, contains energy, and its presence precludes a classical "true vacuum". Is the above statement true or false? Justify your inclusion with not more than ten examples. ii. Explain the significant of the Curl of a vector and discuss what exactly is the essence of the del symbol with an x next to it, iii. Discuss the divergence and slope of the curl. Support your response with not more than five mathematical proofs.

i. A field occupies space, contains energy, and its presence precludes a classical "true vacuum". Is the above statement true or false? Justify your inclusion with not more than ten examples. ii. Explain the significant of the Curl of a vector and discuss what exactly is the essence of the del symbol with an x next to it, iii. Discuss the divergence and slope of the curl. Support your response with not more than five mathematical proofs.