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Chapter 14: Q. 11 (page 1095)

What is the difference between the graphs of

G(x,y)=xi+yjandF(x,y)=鈭�xi+(-y)j

Short Answer

Expert verified

The difference between the graphs are F(x,y)=-G(x,y);at(0,0).

Step by step solution

01

Step 1.Given Information

What is the difference between the graphs of

G(x,y)=xi+yjandF(x,y)=鈭�xi+(-y)j

02

Step 2. The given vector is G(x,y)=xi+yj and F(x,y)=−xi+(-y)j.

Foreverypoint(x,y)鈭�鈩�2WecanwriteF(x,y)asF(x,y)=鈭�xi+(-y)jF(x,y)=鈭�xi-yjF(x,y)=鈭�(xi+yj)AsweknowG(x,y)=xi+yjSowecanwriteF(x,y)=-G(x,y)HenceF(x,y)=-G(x,y);at(0,0)

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