b) Show that the force field F(x, y, z) = 3x^2z i + 2y ln z j + (y^2/z + x^3) k is independent of path and find its potential function. Hence, evaluate ?_C F · dr, where C is a curve with parametrization r(t) = t i + t j + t^2 k for 1 ? t ? e.
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A force field F is conservative if its curl is zero, i.e., curl(F) = 0. 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 For the given force field F(x, y, Show more…
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