Use the Curl Test to Determine Whether the Following Vector

Multiple Choice

Use the curl test to determine whether the following vector field is a gradient field. $\vec { F } = y ^ { 3 } z ^ { 2 } \vec { i } + \left( 4 y ^ { 2 } x z ^ { 2 } + 4 y z ^ { 3 } \right) \vec { j } + \left( 2 x y ^ { 3 } z + 3 y ^ { 2 } z ^ { 2 } \right) \vec { k }$

A) Only at the origin
B) No
C) Yes