Chapter 14: Q. 22 (page 1132)

$Compute the divergence of the vector fields in Exercises 17 - 22 . F (x, y, z) = {xe}^{yz} i + {ye}^{xz} j + {ze}^{xy} k$

Short Answer

Expert verified

$div F = e^{yz} + e^{xz} + e^{xy}$

Step by step solution

Step 1. Given information is:

$F (x, y, z) = {xe}^{yz} i + {ye}^{xz} j + {ze}^{xy} k$

Step 2. Divergence of vector field

$If F (x, y, z) = f_{1} (x, y, z) i + f_{2} (x, y, z) j + f_{3} (x, y, z) k, then div F = \frac{\partial f_{1}}{\partial x} + \frac{\partial f_{2}}{\partial y} + \frac{\partial f_{3}}{\partial z} Here, F (x, y, z) = {xe}^{yz} i + {ye}^{xz} j + {ze}^{xy} k Compare this with, F (x, y, z) = f_{1} (x, y, z) i + f_{2} (x, y, z) j + f_{3} (x, y, z) k Then, f_{1} (x, y, z) = {xe}^{yz}, f_{2} (x, y, z) = {ye}^{xz}, f_{3} (x, y, z) = {ze}^{xy} div F = \frac{\partial f_{1}}{\partial x} + \frac{\partial f_{2}}{\partial y} + \frac{\partial f_{3}}{\partial z} = \frac{\partial ({xe}^{yz})}{\partial x} + \frac{\partial ({ye}^{xz})}{\partial y} + \frac{\partial ({ze}^{xy})}{\partial z} = e^{yz} + e^{xz} + e^{xy}$

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$Compute the divergence of the vector fields in Exercises 17 - 22 . F (x, y, z) = {xe}^{yz} i + {ye}^{xz} j + {ze}^{xy} k$

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Divergence of vector field

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ComputethedivergenceofthevectorfieldsinExercises17–22.F(x,y,z)=xeyzi+yexzj+zexyk

Short Answer

Step by step solution

Step 1. Given information is:

Step 2. Divergence of vector field

One App. One Place for Learning.

Most popular questions from this chapter

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$Compute the divergence of the vector fields in Exercises 17 - 22 . F (x, y, z) = {xe}^{yz} i + {ye}^{xz} j + {ze}^{xy} k$