Solve the Problem $a , b$ And $c$ That Make Gradient Field

question 176

Short Answer

Solve the problem.
-Find the values of $a , b$ and $c$ that make $F = - 9 y ^ { 4 } z ^ { 10 } \left( a x ^ { 7 } + b x ^ { 8 } \right) i - 36 y ^ { 3 } z ^ { 10 } \left( 7 x ^ { 8 } - 7 x ^ { 9 } \right) j + c y ^ { 4 } z ^ { 9 } \left( 7 x ^ { 8 } - 7 x ^ { 9 } \right) \mathbf { k } a$ gradient field.

---

Definitions:

Endocrine Gland

Endocrine system glands that secrete hormones directly into the bloodstream to regulate different body functions.

Epithelial Surface

The layer of cells covering the surfaces of the body, including the skin, organs, and internal passageways.

Bloodstream

The flowing blood within the circulatory system of the body, transporting oxygen, nutrients, and waste products.

Collagenous Fibers

Strong, flexible fibers made of collagen that are a major component of connective tissue in the body.