Consider the circulation of the vector fields in parts (a)(c) around the sets of closed

Chapter 20, Problem 48

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Consider the circulation of the vector fields in parts (a)(c) around the sets of closed curves in (I)(V). For whichof the sets, (I)(V), is the circulation zero on every curve?(I) All closed curves in the xy-plane.(II) All closed curves in the yz-plane.(III) All closed curves in the xz-plane.(IV) All closed curves in the plane x + y + z = 0.(V) All closed curves in all planes of the form mx +ny = d, where m, n, d are constants.(a) F = yi + xj (b) G = yi + xj(c) H = zj

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