Suppose F = (P(x, y, z), Q(x, y, z,), R(x, y, z)), is conservative vector field. Here P, Q, R are such that their second derivatives are continuous. Prove that ƏQ - Əx ӘР ду = 0
Suppose F = (P(x, y, z), Q(x, y, z,), R(x, y, z)), is conservative vector field. Here P, Q, R are such that their second derivatives are continuous. Prove that ƏQ - Əx ӘР ду = 0
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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![Suppose \(\vec{F} = (P(x, y, z), Q(x, y, z), R(x, y, z))\) is a conservative vector field. Here \(P, Q, R\) are such that their second derivatives are continuous. Prove that
\[
\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = 0
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1d5e88e6-b1af-4aea-9b08-2dadd85f5e2c%2F41b6831e-6ea3-4c89-933c-3431e7c82460%2Fvy7qr18_processed.png&w=3840&q=75)
Transcribed Image Text:Suppose \(\vec{F} = (P(x, y, z), Q(x, y, z), R(x, y, z))\) is a conservative vector field. Here \(P, Q, R\) are such that their second derivatives are continuous. Prove that
\[
\frac{\partial Q}{\partial x} - \frac{\partial P}{\partial y} = 0
\]
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