- Iii Prove That If F Is A Differentiable Cl Vector Field On All Of R3 With V F 0 Then There Exists A C1 Vector 1 (32.51 KiB) Viewed 36 times
= = = (iii) Prove that if F is a differentiable Cl vector field on all of R3 with V.F = 0, then there exists a C1 vector
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= = = (iii) Prove that if F is a differentiable Cl vector field on all of R3 with V.F = 0, then there exists a C1 vector
= = = (iii) Prove that if F is a differentiable Cl vector field on all of R3 with V.F = 0, then there exists a C1 vector field G with F = VxG. Hint: if F = Fii+F2j+Fzk, then define G = G2j + G3k and find equations for G2 and G3 in terms of F1, F2, F3. Alternatively, show that G1 = 0 = t Gz = [* F3(t, y, z)dt ES" F(0, 1, 2)dt +- SP G3 = (t- F2(t, y, z)dt provides a possible solution for G. (10 marks)
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