For each of the following vector fields, find its curl and determine if it is a gradient field. (a) F = 5yzi+ (5xz + z²) j + (5xy+2yz) k curl F = 0 Fis a gradient field (b) G = (10xy+x³) i+ (5x² + z²) }+ (2yz — 4z) k curl Ğ Ġ is a gradient field (c) H = 5yzi+ (22- 5xz) + (5xy + 2yz) k curl H = [ His not a gradient field
For each of the following vector fields, find its curl and determine if it is a gradient field. (a) F = 5yzi+ (5xz + z²) j + (5xy+2yz) k curl F = 0 Fis a gradient field (b) G = (10xy+x³) i+ (5x² + z²) }+ (2yz — 4z) k curl Ğ Ġ is a gradient field (c) H = 5yzi+ (22- 5xz) + (5xy + 2yz) k curl H = [ His not a gradient field
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
Question
![For each of the following vector fields, find its curl and determine if it is a gradient field.
(a) F = 5yzi+ (5xz + z²) j + (5xy+2yz) k
curl F = 0
Fis a gradient field
(b) G = (10xy+x³) i+ (5x² + z²) }+ (2yz — 4z) k
curl Ğ
Ġ is a gradient field
(c) H = 5yzi+ (22- 5xz) + (5xy + 2yz) k
curl H = [
His not a gradient field](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F92927d35-c8d4-4d26-a361-d4932ab03fa8%2F1a2df5d1-08c2-413b-95dc-674ba645a7cf%2F9a3ytr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:For each of the following vector fields, find its curl and determine if it is a gradient field.
(a) F = 5yzi+ (5xz + z²) j + (5xy+2yz) k
curl F = 0
Fis a gradient field
(b) G = (10xy+x³) i+ (5x² + z²) }+ (2yz — 4z) k
curl Ğ
Ġ is a gradient field
(c) H = 5yzi+ (22- 5xz) + (5xy + 2yz) k
curl H = [
His not a gradient field
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