GATE 2023 Civil Engineering Q11

Question

Let $\phi$ be a scalar field, and $\mathbf{u}$ be a vector field. Which of the following identities is true for $	ext{div}(\phi\mathbf{u})$?

Accepted Answer

$	ext{div}(\phi\mathbf{u}) = \phi	ext{div}(\mathbf{u}) + \mathbf{u} \cdot 	ext{grad}(\phi)$

Answer

$	ext{div}(\phi\mathbf{u}) = \phi	ext{div}(\mathbf{u}) + \mathbf{u} 	imes 	ext{grad}(\phi)$

Answer

$	ext{div}(\phi\mathbf{u}) = \phi	ext{grad}(\mathbf{u}) + \mathbf{u} \cdot 	ext{grad}(\phi)$

Answer

$	ext{div}(\phi\mathbf{u}) = \phi	ext{grad}(\mathbf{u}) + \mathbf{u} 	imes 	ext{grad}(\phi)$