EXAMPLE 2 Show that the vector field F(x, y, z) = 4xzi + 5xyzj – y²k is not conservative. SOLUTION Using this equation, we have j a curl F = Vx F = i k ax ду az 5xyz -y? 4xz ду az (Sxyz) – (4x2) K + ду (-2y - (0 - 4x)j + (5yz - 0)k This shows that curl F = v0 and so F is not conservative.

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