Determine Whether or Not Vector Field Is Conservative $f$ Such That $\mathbf { F } = \nabla f$

question 55

Short Answer

Determine whether or not vector field is conservative. If it is conservative, find a function $f$ such that $\mathbf { F } = \nabla f$ .
$$\mathbf { F } ( x , y , z ) = 5 z y \mathbf { i } + 5 x z \mathbf { j } + 5 x y \mathbf { k }$$

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Definitions:

Arthropoda

A phylum of invertebrate animals that includes insects, arachnids, myriapods, and crustaceans, characterized by an exoskeleton, segmented body, and jointed appendages.

Jointed Appendages

Jointed appendages are limbs or structures that are segmented and connected by joints, allowing for a range of movements, characteristic of arthropods.

Nervous System

The network of nerve cells and fibers that transmits signals between parts of the body, coordinating actions and sensory information.

Flatworms

A phylum of simple, soft-bodied invertebrate animals known for their bilateral symmetry and lack of a body cavity.