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For each of the following decide whether the vector field could be a gradient vector field. Be sure that you can justify your answer. (a) F(x, y, z) = 2x i + 2zj F(x, y, z) is not a gradient vector field (b) F(x, y, z) = (3z, 0, 3x) F(x, y, z) is a gradient vector field (c) F(x, y, z) = √² + √2²42²³ + 7 +2² F(x, y, z) is not a gradient vector field k √²+2

For each of the following decide whether the vector field could be a gradient vector field. Be sure that you can justify your answer. (a) F(x, y, z) = 2x i + 2zj F(x, y, z) is not a gradient vector field (b) F(x, y, z) = (3z, 0, 3x) F(x, y, z) is a gradient vector field (c) F(x, y, z) = √² + √2²42²³ + 7 +2² F(x, y, z) is not a gradient vector field k √²+2

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter9: Vectors In Two And Three Dimensions
Section9.FOM: Focus On Modeling: Vectors Fields
Problem 11P
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For each of the following decide whether the vector field could be a gradient vector field. Be sure that you can justify your answer. (a) F(x, y, z) = 2x7+2zj F(x, y, z) is not a gradient vector field (b) F(x, y, z) = (3z, 0, 3x) F(x, y, z) is a gradient vector field 4z 4y 4x (c) F(x, y, z) = 7 √²+2+²+2 j+ k F(x, y, z) is not a gradient vector field (d) F(x, y, z) = (3yz, 3xz, 3xy) F(x, y, z) is not a gradient vector field
Transcribed Image Text:For each of the following decide whether the vector field could be a gradient vector field. Be sure that you can justify your answer. (a) F(x, y, z) = 2x7+2zj F(x, y, z) is not a gradient vector field (b) F(x, y, z) = (3z, 0, 3x) F(x, y, z) is a gradient vector field 4z 4y 4x (c) F(x, y, z) = 7 √²+2+²+2 j+ k F(x, y, z) is not a gradient vector field (d) F(x, y, z) = (3yz, 3xz, 3xy) F(x, y, z) is not a gradient vector field
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