Question: In parts (a)(h), prove the property for vector fields F and G and scalar function f. (Assume that the required partial derivatives are continuous.) (a)

In parts (a)–(h), prove the property for vector fields F and G and scalar function f. (Assume that the required partial derivatives are continuous.)

(a) curl(F + G) = curl F + curl G (b) curl(vf)

= V (Vf) = 0 (c) div(F + G) = div F

(a) curl(F + G) = curl F + curl G (b) curl(vf) = V (Vf) = 0 (c) div(F + G) = div F + div G (d) div(F x G) = (curl F) G - F. (curl G) (e) x [Vf+ (V x F)] = V (V x F) (f) x (fF) = f(V x F) + (vf) F (g) div(fF) = f div F + Vf. F (h) div(curl F) = 0 (Theorem 15.3)

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a To prove curlFG curl F curl G we can use the properties of the curl and the product rule for taking derivatives Let F P i Q j R k and G U i V j W k be vector fields The curl of F is given by curl F ... View full answer

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