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In Cartesian coordinates, a vector field takes the form F= 2xzi+ 2yzj+ (x²+y²)k a. State whether F is conservative, and give a one-sentence justification for your statement 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 b. parametric representation x=at, y=bt, z=ct (0StS1). C.Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(x, y, z) corresponding to F, such that F=-VU.

In Cartesian coordinates, a vector field takes the form F= 2xzi+ 2yzj+ (x²+y²)k a. State whether F is conservative, and give a one-sentence justification for your statement 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 b. parametric representation x=at, y=bt, z=ct (0StS1). C.Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(x, y, z) corresponding to F, such that F=-VU.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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In Cartesian coordinates, a vector field takes the form F= 2xzi+ 2yzj+ (X2+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 x=at, y=bt, z=ct (0sts1). c. Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(x, y, z) corresponding to F, such that F=-VU.
Transcribed Image Text:In Cartesian coordinates, a vector field takes the form F= 2xzi+ 2yzj+ (X2+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 x=at, y=bt, z=ct (0sts1). c. Given that the point (a, b, c) could be anywhere, use your answer to part (b) to find the scalar potential function U(x, y, z) corresponding to F, such that F=-VU.
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