Explain why or why not Determine whether the following statements are true and give an explanation or counterexample.
a. A paddle wheel with its axis in the direction 〈0.1, –1〉 would not spin when put in the
b. Stokes’ Theorem relates the flux of a vector field F across a surface to the values of F on the boundary of the surface.
c. A vector field of the form F = 〈a + f(x), b + g(y), c + h(z)〉, where a, b, and c are constants, has zero circulation on a closed curve.
d. If a vector field has zero circulation on all simple closed smooth curves C in a region D, then F is conservative on D.
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Calculus: Early Transcendentals (3rd Edition)
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