Problem 15 Calculate the divergence of the following vector functions:(a) v,=x+ 3xz 9- 2xz2.(b) v, = xyi + 2yz ý + 3zx î.(e) v, y &+ (2xy+z)9+2yz2Problem 16 Sketch the vector functionand compute its divergence. The answer may surprise you...can you explain it?Problem 17 In two dimensions, show that the divergence transforms as a scalarunder rotations. [Hint: Use Eq. 29 to determine , and ū., and the method ofProb. 14 to calculate the derivatives. Your aim is to show that au,/ay +av,/az =au,/ay + av/az.]%3D

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Problem 15 Calculate the divergence of the following vector functions: (a) v,x+3xz²ŷ - 2xz2. (b) v, xy&+2yzý + 3zx i. (e) v, y&+ (2xy +z)9+2yza. Problem 16 Sketch the vector function and compute its divergence. The answer may surprise you..can you explain it? Problem 17 lIn two dimensions, show that the divergence transforms as a scalar under rotations. [Hint: Use Eq. 29 to determine v, and v, and the method of Prob. 14 to calculate the derivatives. Your aim is to show that a0,/ay +av,/az - au,/ay+av/az.J

Problem 15 Calculate the divergence of the following vector functions: (a) v,x+3xz²ŷ - 2xz2. (b) v, xy&+2yzý + 3zx i. (e) v, y&+ (2xy +z)9+2yza. Problem 16 Sketch the vector function and compute its divergence. The answer may surprise you..can you explain it? Problem 17 lIn two dimensions, show that the divergence transforms as a scalar under rotations. [Hint: Use Eq. 29 to determine v, and v, and the method of Prob. 14 to calculate the derivatives. Your aim is to show that a0,/ay +av,/az - au,/ay+av/az.J

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter1: Introduction And Vectors

Section: Chapter Questions

Problem 7CQ

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