 6.3.1: Consider the line integral C z2 dx + 2y dy + xz dz. (a) Evaluate th...
 6.3.2: Let F = 2x y i + (x 2 + z2) j + 2yz k. (a) Calculate C F ds, where ...
 6.3.3: In Exercises 317, determine whether the given vector field F is con...
 6.3.4: In Exercises 317, determine whether the given vector field F is con...
 6.3.5: In Exercises 317, determine whether the given vector field F is con...
 6.3.6: In Exercises 317, determine whether the given vector field F is con...
 6.3.7: In Exercises 317, determine whether the given vector field F is con...
 6.3.8: In Exercises 317, determine whether the given vector field F is con...
 6.3.9: In Exercises 317, determine whether the given vector field F is con...
 6.3.10: In Exercises 317, determine whether the given vector field F is con...
 6.3.11: In Exercises 317, determine whether the given vector field F is con...
 6.3.12: In Exercises 317, determine whether the given vector field F is con...
 6.3.13: In Exercises 317, determine whether the given vector field F is con...
 6.3.14: In Exercises 317, determine whether the given vector field F is con...
 6.3.15: In Exercises 317, determine whether the given vector field F is con...
 6.3.16: In Exercises 317, determine whether the given vector field F is con...
 6.3.17: In Exercises 317, determine whether the given vector field F is con...
 6.3.18: Of the two vector fields F = x y2z3 i + 2x 2 y j + 3x 2 y2z2 k and ...
 6.3.19: (a) Let f be a function of class C1 defined on a connected domain i...
 6.3.20: Find all functions M(x, y) such that the vector field F = M(x, y) i...
 6.3.21: Find all functions N(x, y) such that the vector field F = (ye2x + 3...
 6.3.22: Let G(x, y) = (xex + y2) i + x y j. Find all functions g(x) such th...
 6.3.23: Find all functions N(x, y,z) such that the vector field F = (x 3 y ...
 6.3.24: For what values of the constants a and b will the vector field F = ...
 6.3.25: Let F = x 2 i + cos y sin z j + sin y cosz k. (a) Show that F is co...
 6.3.26: Show that the line integrals in Exercises 2628 are path independent...
 6.3.27: Show that the line integrals in Exercises 2628 are path independent...
 6.3.28: Show that the line integrals in Exercises 2628 are path independent...
 6.3.29: In Exercises 2932, find the work done by the given vector field F i...
 6.3.30: In Exercises 2932, find the work done by the given vector field F i...
 6.3.31: In Exercises 2932, find the work done by the given vector field F i...
 6.3.32: In Exercises 2932, find the work done by the given vector field F i...
 6.3.33: (a) Determine where the vector field F = x + x y2 y2 i x 2 + 1 y3 j...
 6.3.34: Let f , g, and h be functions of class C1 of a single variable. (a)...
 6.3.35: Consider the vector field F = (2x + z) cos (x 2 + x z) i (z + 1) si...
 6.3.36: Consider the vector field G = (2x + z) cos (x 2 + x z) i + (x (z + ...
 6.3.37: Let F be the gravitational force field of a mass M on a particle of...
Solutions for Chapter 6.3: Conservative Vector Fields
Full solutions for Vector Calculus  4th Edition
ISBN: 9780321780652
Solutions for Chapter 6.3: Conservative Vector Fields
Get Full SolutionsSince 37 problems in chapter 6.3: Conservative Vector Fields have been answered, more than 13559 students have viewed full stepbystep solutions from this chapter. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Vector Calculus, edition: 4. Vector Calculus was written by and is associated to the ISBN: 9780321780652. Chapter 6.3: Conservative Vector Fields includes 37 full stepbystep solutions.

Angle of depression
The acute angle formed by the line of sight (downward) and the horizontal

Annuity
A sequence of equal periodic payments.

Common difference
See Arithmetic sequence.

Complements or complementary angles
Two angles of positive measure whose sum is 90°

Data
Facts collected for statistical purposes (singular form is datum)

Extraneous solution
Any solution of the resulting equation that is not a solution of the original equation.

Horizontal component
See Component form of a vector.

Horizontal translation
A shift of a graph to the left or right.

Line of travel
The path along which an object travels

Linear equation in x
An equation that can be written in the form ax + b = 0, where a and b are real numbers and a Z 0

Midpoint (in a coordinate plane)
For the line segment with endpoints (a,b) and (c,d), (aa + c2 ,b + d2)

Obtuse triangle
A triangle in which one angle is greater than 90°.

Order of magnitude (of n)
log n.

Parallelogram representation of vector addition
Geometric representation of vector addition using the parallelogram determined by the position vectors.

Sequence
See Finite sequence, Infinite sequence.

Solve by elimination or substitution
Methods for solving systems of linear equations.

Transitive property
If a = b and b = c , then a = c. Similar properties hold for the inequality symbols <, >, ?, ?.

Vertex of a cone
See Right circular cone.

Vertical component
See Component form of a vector.

Zero factor property
If ab = 0 , then either a = 0 or b = 0.