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Chapter 14: Q. 7 (page 1095)

What does it mean to say that a vector field is conservative?

Short Answer

Expert verified

A conservative vector field F is a vector field that can be written as the gradient of some function f.

Step by step solution

01

Step 1.Given Information

What does it mean to say that a vector field is conservative?

02

Step 2. A vector field is conservative 

If a vector field can be described as a gradient, it offers a number of mathematically appealing properties, including the ability to be easily integrated along curves. Such fields are referred to as conservative vector fields.

A vector field that is conservative. F is a vector field that represents the gradient of a function f.

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Most popular questions from this chapter

Calculus of vector-valued functions: Calculate each of the following.

ddt(r(t)),wherer(t)=3cos2ti+5tj+tt2+1k

Find the work done by the vector field

F(x,y)=x3y2i+(y-x)j

in moving an object around the triangle with vertices (1,1),(2,2), and (3,1), starting and ending at (2,2).

ComputethedivergenceofthevectorfieldsinExercises17鈥�22.G(x,y,z)=yz2i鈭�xsinzj+x2exyk

Use the same vector field as in Exercise 13, and compute the k-component of the curl of F(x, y).

Make a chart of all the new notation, definitions, and theorems in this section, including what each new item means in terms you already understand.
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