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(Solved): Using tensor notation, verify the vector identity \[ (\nabla \times \vec{V}) \times \vec{V}=(\vec{ ...


Using tensor notation, verify the vector identity \[ (\nabla \times \vec{V}) \times \vec{V}=(\vec{V} \cdot \nabla) \vec{V}-\n

Using tensor notation, verify the vector identity \[ (\nabla \times \vec{V}) \times \vec{V}=(\vec{V} \cdot \nabla) \vec{V}-\nabla\left(\frac{1}{2} V^{2}\right) \]


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?A=??A+??A?A=??A+??A where ??A??A is a k?1k?1 vector field, and ??A??A is a k+1k+1 vector field. If k=0k=0, then ?A=??A?A=??A by definition. Similarly, if k=nk=n, then ?A=??A?A=??A. Useful identity: ??(??A)=0??(??A)=0
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