題組內容
5. Consider a force field \( \vec{\mathbf{F}} = (2xy + z^3)\vec{i} + x^2\vec{j} + 3xz^2\vec{k} \), and answer the following questions:
(a) \( (5\%) \) Show that the force is conservative.
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5. Consider a force field \( \vec{\mathbf{F}} = (2xy + z^3)\vec{i} + x^2\vec{j} + 3xz^2\vec{k} \), and answer the following questions:
(a) \( (5\%) \) Show that the force is conservative.