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Chapter 14: Q 2 (page 1153)

For any vector Ffield in R2 or R3,

localid="1651016641773" divcurlF=______=______.

Short Answer

Expert verified

The required answer is :-

For any vector field in R2or R3

divcurlF=鈭�路(鈭�脳F)=0.

Step by step solution

01

Step 1. Given Information

We have given the following statement :-

divcurlF=______=______.

02

Step 2. Complete the statement

We have to complete the given statement :-

divcurlF=______=______.

If

F=F1(x,y,z),F2(x,y,z)inR2orF=F1(x,y,z),F2(x,y,z),F3(x,y,z)inR3

Here Fi's, i=1,2,3have continuous second order partial derivative.

We know that curlF=鈭�脳Fand divF=鈭�路F

So that div(curlF)=鈭�路鈭�脳F

We can easily get that :-

鈭�脳F=0鈬�鈭�路鈭�脳F=0

So our final answer is :-

divcurlF=鈭�路(鈭�脳F)=0.

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Most popular questions from this chapter

F=xln(xz),5z,1y2+1 , where S is the region of the plane with equation 12x鈭�9y+3z=10, where 2鈮�x鈮�3and 5鈮�y鈮�10, with n pointing upwards.

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Sis the portion of the surface determined by x=9-y2-z2 that lies on the positive side of the yzplane (i.e., where x鈮�0)

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