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 & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 31E

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