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6. Let F= Fi + F2j+F3k be a vector field and let j k VXF= 8 Әх F₁ F2 F3 OF3 OF -i (F30/F/2) -j (01/02) + k (31/2_017). ду дz ду A vector field F is said to be conservative if V x F = 0. Show that the vector field in Problem 5 is conservative.

6. Let F= Fi + F2j+F3k be a vector field and let j k VXF= 8 Әх F₁ F2 F3 OF3 OF -i (F30/F/2) -j (01/02) + k (31/2_017). ду дz ду A vector field F is said to be conservative if V x F = 0. Show that the vector field in Problem 5 is conservative.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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6. Let F = Fi + Fzj + F3k be a vector field and let 2 j Ә 8 Ә Әх ду дz F₁ F2 F3 VXF= = (F) - (^_0F) +*( дz A vector field F is said to be conservative if V x F = 0. Show that the vector field in Problem 5 is conservative. а ). ду OF OF
Transcribed Image Text:6. Let F = Fi + Fzj + F3k be a vector field and let 2 j Ә 8 Ә Әх ду дz F₁ F2 F3 VXF= = (F) - (^_0F) +*( дz A vector field F is said to be conservative if V x F = 0. Show that the vector field in Problem 5 is conservative. а ). ду OF OF
5. Find the potential function o corresponding to the vector field F(x, y, z) = (-2xy² − 3x²z)i + (2³ – 2x²y)j + (3yz²x³)k.
Transcribed Image Text:5. Find the potential function o corresponding to the vector field F(x, y, z) = (-2xy² − 3x²z)i + (2³ – 2x²y)j + (3yz²x³)k.
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