For each of the following vector fields F , decide whether it is conservative or not by computing curl F . Type in a potential function f (that is, ?f = F). If it is not conservative, type N. A. F (x, y) = (-14x + 5y) i + (5x + 6y) j f (x, y) = B. F (x, y) = -7yi - 6xj f (x, y) = C. F (x, y, z) = -7xi - 6yj + k f (x, y, z) = D. F (x, y) = (-7 sin y) i + (10y - 7x cos y) j f (x, y) = E. F (x, y, z) = -7x^2i + 5y^2j + 3z^2k f (x, y, z) = Note: Your answers should be either expressions of x, y and z (e.g. "3xy + 2yz"), or the letter "N"
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The curl of a vector field F = P(x, y, z)i + Q(x, y, z)j + R(x, y, z)k is given by: curl(F) = (∂R/∂y - ∂Q/∂z)i + (∂P/∂z - ∂R/∂x)j + (∂Q/∂x - ∂P/∂y)k A. F(x, y) = (14x)i + (5x^2 + 6y)j Since this is a 2D vector field, we can set R(x, y) = 0. Then, the curl Show more…
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