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GATE2015-3-24

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Let $\phi$ be an arbitrary smooth real valued scalar function and $\overrightarrow{V}$ be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following is an identity?

  1. Curl$(\phi \overrightarrow{V})$ = $\bigtriangledown$($\phi$ Div$\overrightarrow{V}$)
  2. Div$\overrightarrow{V}=0$
  3. Div Curl$\overrightarrow{V}=0$
  4. Div($(\phi \overrightarrow{V})$ ) = $\phi$ Div$\overrightarrow{V}$
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