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In Cartesian coordinates, a vector field takes the form F = 2rz i+2yz j+ (z + y?)k (a) State whether F is conservative, and give a one-sentence justification for your statement. (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation I = at, y = bt, z = ct (0

In Cartesian coordinates, a vector field takes the form F = 2rz i+2yz j+ (z + y?)k (a) State whether F is conservative, and give a one-sentence justification for your statement. (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation I = at, y = bt, z = ct (0

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter4: Vector Spaces
Section4.1: Vector In R^n
Problem 28E
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Q6, a, b, c
In Cartesian coordinates, a vector field takes the form 2rzi+ 2yzj+ (r² + y²) k (a) State whether F is conservative, and give a one-sentence justification for your statement. (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation I = at, y= bt, z = ct (0 <t < 1). (c) Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(r, y, z) corresponding to F, such that F = -VU.
Transcribed Image Text:In Cartesian coordinates, a vector field takes the form 2rzi+ 2yzj+ (r² + y²) k (a) State whether F is conservative, and give a one-sentence justification for your statement. (b) Calculate the line integral of F along a straight-line path starting at the origin and ending at the point (a, b, c). This path has the parametric representation I = at, y= bt, z = ct (0 <t < 1). (c) Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(r, y, z) corresponding to F, such that F = -VU.
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