Use the Curl Test to Determine Whether the Following Vector

question 3

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

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Definitions:

Disease-resistant

The ability of an organism to prevent infection or resist the effects of disease-causing pathogens through natural or genetically modified traits.

Chemical Pesticides

Substances used to kill or control the population of pests that can harm crops, animals, and humans, made from synthetic chemicals.

Municipalities

Local government entities that are responsible for providing local services, infrastructure, and governance within their specified areas.

Rodenticides

Chemicals used to kill rodents, often used in pest control to protect crops or prevent disease spread.