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10 Consider the vector field F(x, y, z) = Ꮖ = ( ² + 2², 5, 1/2 + 2²) defined on the set 5. Then N = {(x, y, z) = R³ : −5 < x < 0, 0 < y < 6, 0 ≤ z < 1 + x² + y² }. (A) curl F (0, 0, 0) in (B) curl F = (0, 0, 0) in 2, but F is not conservative in since is not simply connected 1 (C) the function & defined by 4(x, y, z) = log x - - +5y, V(x, y, z) = n, is a potential of φ Fin Ω (D) F is conservative in

10 Consider the vector field F(x, y, z) = Ꮖ = ( ² + 2², 5, 1/2 + 2²) defined on the set 5. Then N = {(x, y, z) = R³ : −5 < x < 0, 0 < y < 6, 0 ≤ z < 1 + x² + y² }. (A) curl F (0, 0, 0) in (B) curl F = (0, 0, 0) in 2, but F is not conservative in since is not simply connected 1 (C) the function & defined by 4(x, y, z) = log x - - +5y, V(x, y, z) = n, is a potential of φ Fin Ω (D) F is conservative in

Elementary Linear Algebra (MindTap Course List)
Elementary Linear Algebra (MindTap Course List)
8th Edition
ISBN:9781305658004
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Inner Product Spaces
Section5.3: Orthonormal Bases:gram-schmidt Process
Problem 71E
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the answer is D
could you explain how using the curl
and also please disprove each option that is wrong

10 Consider the vector field F(x, y, z) = Ꮖ = ( ² + 2², 5, 1/2 + 2²) defined on the set 5. Then N = {(x, y, z) = R³ : −5 < x < 0, 0 < y < 6, 0 ≤ z < 1 + x² + y² }. (A) curl F (0, 0, 0) in (B) curl F = (0, 0, 0) in 2, but F is not conservative in since is not simply connected 1 (C) the function & defined by 4(x, y, z) = log x - - +5y, V(x, y, z) = n, is a potential of φ Fin Ω (D) F is conservative in
Transcribed Image Text:10 Consider the vector field F(x, y, z) = Ꮖ = ( ² + 2², 5, 1/2 + 2²) defined on the set 5. Then N = {(x, y, z) = R³ : −5 < x < 0, 0 < y < 6, 0 ≤ z < 1 + x² + y² }. (A) curl F (0, 0, 0) in (B) curl F = (0, 0, 0) in 2, but F is not conservative in since is not simply connected 1 (C) the function & defined by 4(x, y, z) = log x - - +5y, V(x, y, z) = n, is a potential of φ Fin Ω (D) F is conservative in
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