Let $\vec { a } = a _ { 1 } \vec { i } + \alpha _ { 2 } \vec { i } + \alpha _ { 3 } \vec { i }$

Multiple Choice

Let $\vec { a } = a _ { 1 } \vec { i } + \alpha _ { 2 } \vec { i } + \alpha _ { 3 } \vec { i }$ be a constant vector and f(x, y, z) be a smooth function.Which statement is true?

A) If $\operatorname { div } f \vec { a }$ is a divergence free vector field then $\nabla$ f is parallel to
$\vec { \alpha }$
B) If $\operatorname { div } f \vec { a }$ is not a divergence free vector field then $\nabla$ f is perpendicular to
$\vec { \alpha }$
C) If $\operatorname { div } f \vec { a }$ is a divergence free vector field then $\nabla$ f is perpendicular to
$\vec { \alpha }$
D) If $\operatorname { div } f \vec { a }$ is not a divergence free vector field then $\nabla$ f is parallel to
$\vec { \alpha }$
E) If $\operatorname { div } f \vec { a }$ is a divergence free vector field then $\nabla$ f is constant.