Let ϕ be an arbitrary smooth real valued scalar function and V be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following is an identity?

\({\rm{Div}}\left( {\phi {\rm{\vec V}}} \right) = \phi ~{\rm{Div\vec V}}\)

\({\rm{Curl}}\left( {\phi {\rm{\vec V}}} \right) = \nabla \left( {\phi~ {\rm{Div\vec V}}} \right)\)

Let ϕ be an arbitrary smooth real valued scalar function and V be an

1.	Let ϕ be an arbitrary smooth real valued scalar function and V be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following is an identity?
A.	\({\rm{Curl}}\left( {\phi {\rm{\vec V}}} \right) = \nabla \left( {\phi~ {\rm{Div\vec V}}} \right)\)
B.	\({\rm{Div\vec V}} = 0\)
C.	\({\rm{Div~Curl\vec V}} = 0\)
D.	\({\rm{Div}}\left( {\phi {\rm{\vec V}}} \right) = \phi ~{\rm{Div\vec V}}\)
Answer» D. \({\rm{Div}}\left( {\phi {\rm{\vec V}}} \right) = \phi ~{\rm{Div\vec V}}\)

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Let ϕ be an arbitrary smooth real valued scalar function and V be an arbitrary smooth vector valued function in a three-dimensional space. Which one of the following is an identity?

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