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Chapter 14: Q. 21 (page 1150)

compute the divergence of the given vector field.

F(x,y,z)=xi+yj+zk

Short Answer

Expert verified

The divergence of the vector field is divF=3

Step by step solution

01

Introduction

Take the vector field for example.

F(x,y,z)=xi+yj+zk

The goal is to find the divergence of the vector entered.

Apply the formula,divF=鈭�F1鈭�x+鈭�F2鈭�y+鈭�F3Oz^

Compare the vectors provided. With the vector, F(x,y,z)=xi+yj+zk.

F(x,y,z)=F1(x,y,z)+F2(x,y,z)+F3(x,y,z)

So,F1(x,y,z)=x

F2(x,y,z)=y

F3(x,y,z)=z

02

Explanation

Calculate divF

divF=鈭�F1鈭�x+鈭�F2鈭�y+鈭�F3鈭�z

=鈭�鈭�x(x)+鈭�鈭�y(y)+鈭�鈭�z(z)

=1+1+1

=3

Therefore,role="math" localid="1650784678183" divF=3

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Most popular questions from this chapter

F(x,y,z)=鉄�yz,xz,xy鉄�, where S is the portion of the saddle determined byz=x2鈭�y2 that lies above the region in thexy-plane bounded by the x-axis and the parabola with equationy=1鈭�x2.

Do the vectors in the range of F(x,y)=xi+yjpoint towards or away from the origin?

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