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defined on the set 10 Consider the vector field F(x, y, z) = (= + 2²,5 = +2²) N = {(x, y, z) € R³ : -5 < r < 0,0 < y < 6,0 < z < 1 + x² + y²}. Then (A) curl F ‡ (0, 0, 0) in (2 (B) curl F = (0, 0, 0) in 2, but F is not conservative in 2 since 2 is not simply connected 1 (C) the function defined by (x. y. 2) = log r -+5y, V(r,y,z) €, is a potential of 2 (D) F is conservative in 2

defined on the set 10 Consider the vector field F(x, y, z) = (= + 2²,5 = +2²) N = {(x, y, z) € R³ : -5 < r < 0,0 < y < 6,0 < z < 1 + x² + y²}. Then (A) curl F ‡ (0, 0, 0) in (2 (B) curl F = (0, 0, 0) in 2, but F is not conservative in 2 since 2 is not simply connected 1 (C) the function defined by (x. y. 2) = log r -+5y, V(r,y,z) €, is a potential of 2 (D) F is conservative in 2

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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10 Consider the vector field F(x, y, z) = ( = + z², 5, = + 2²) defined on the set N = {(x, y, z) € R³ : -5 < a < 0,0 < y < 6,0 < z < 1 + x² + y²}. Then (A) curl F ‡ (0, 0, 0) in 2 (B) curl F = (0, 0, 0) in 2, but F is not conservative in 2 since 2 is not simply connected 1 (C) the function 4 defined by (r. y, z) = log r - - + 5y. V(x, y, z) € 9, is a potential of F in Q (D) F is conservative in 2
Transcribed Image Text:10 Consider the vector field F(x, y, z) = ( = + z², 5, = + 2²) defined on the set N = {(x, y, z) € R³ : -5 < a < 0,0 < y < 6,0 < z < 1 + x² + y²}. Then (A) curl F ‡ (0, 0, 0) in 2 (B) curl F = (0, 0, 0) in 2, but F is not conservative in 2 since 2 is not simply connected 1 (C) the function 4 defined by (r. y, z) = log r - - + 5y. V(x, y, z) € 9, is a potential of F in Q (D) F is conservative in 2
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