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How can the following identity be proven?

$$\nabla(\vec{A} \cdot \vec{B}) = \vec{A} \times(\nabla \times \vec{B}) + \vec{B} \times(\nabla \times \vec{A}) + (\vec{A}\cdot \nabla)\vec{B} + (\vec{B} \cdot \nabla)\vec{A}$$

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    Hello, Ahsan, and welcome to math.SE. Since you are new, I want to give you some advice about the site: **To get the best possible answers, you should explain what your thoughts on the problem are so far**. That way, people won't tell you things you already know, and they can write answers at an appropriate level; also, people are much more willing to help you if you show that you've tried the problem yourself.2012-07-13

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