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Chapter 14: Q. 19 (page 1132)

ComputethedivergenceofthevectorfieldsinExercises17鈥�22.G(x,y,z)=yz2i鈭�xsinzj+x2exyk

Short Answer

Expert verified

divG=0

Step by step solution

01

Step 1. Given information is: 

G(x,y,z)=yz2i鈭�xsinzj+x2exyk

02

Step 2. Divergence of vector field

IfG(x,y,z)=g1(x,y,z)i+g2(x,y,z)j+g3(x,y,z)k,thendivG=鈭�g1鈭�x+鈭�g2鈭�y+鈭�g3鈭�zHere,G(x,y,z)=yz2i鈭�xsinzj+x2exykComparethiswith,G(x,y,z)=g1(x,y,z)i+g2(x,y,z)j+g3(x,y,z)kThen,g1(x,y,z)=yz2,g2(x,y,z)=鈭�xsinz,g3(x,y,z)k=x2exydivG=鈭�g1鈭�x+鈭�g2鈭�y+鈭�g3鈭�z=鈭�(yz2)鈭�x+鈭�(鈭�xsinz)鈭�y+鈭�(x2exy)鈭�z=0

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