IV. Let F(r, y, z) be three dimensional irrotational vector field (zero curl). Let C be the curve parametrized by r(t) = (cos t, sin t, 1), for t e [0, 27]. Suppose that f F · dr 1. Is it possible that F is defined on the entire R3? Explain!

Advanced Engineering Mathematics
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ISBN:9780470458365
Author:Erwin Kreyszig
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Chapter2: Second-order Linear Odes
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IV. Let F(xr, y, z) be three dimensional irrotational vector field (zero curl). Let C be the
curve parametrized by r(t) = (cost, sin t, 1), for t € [0, 27]. Suppose that ƒ F · dr = 1.
Is it possible that F is defined on the entire R3? Explain!
Transcribed Image Text:IV. Let F(xr, y, z) be three dimensional irrotational vector field (zero curl). Let C be the curve parametrized by r(t) = (cost, sin t, 1), for t € [0, 27]. Suppose that ƒ F · dr = 1. Is it possible that F is defined on the entire R3? Explain!
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