Let F be any vector field of the form F = f (x)i+g (y)j+h (z) k and let G be any vector field of the form G = f (y, z)i+g(x, z)j+ h(x, y) k. Indicate whether the following statements are true or false by placing "T" or "F" to the left of the statement. 1. F is irrotational 2. G is irrotational 3. F is incompressible 4. G is incompressible

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Q: 1. Let f: R" → R be the function f(x) = cx+b for some fixed vector c ER" and scalar b. Show that f…

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Q: 1. Prove that (a) ▼ × (▼ƒ) = 0 for any C² function ƒ : U → R;

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A: To find the divergence of the field F.F=-4x5i+2y5j-8z5k

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Q: 4. Let ƒ,g be C² scalar fields on R³. Verify that V x (ƒVg) = Vƒ × Vg. V × (ƒVg+gVf). V· (SVg) =…

A: As give by the question There are given that the scalar field is f, g be C2 on ℝ3. And, In the above…

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A: Step 1:  Step 2:  Step 3:

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