Find the curl and of the vector field. F(x,y,z)=(x+yz)i+(y+xz)j+(z+xy)k

inlays85k5

inlays85k5

Answered question

2021-11-13

Find the curl and of the vector field.
F(x,y,z)=(x+yz)i+(y+xz)j+(z+xy)k

Answer & Explanation

Troy Lesure

Troy Lesure

Beginner2021-11-14Added 26 answers

By definition curl F=×F
If F=Pi+Qi+Rk
Then
F=[ijkddxddyddzPQR]
Which is
F=(dRdydQdz)i+(dPdzdRdx)j+(dQdxdPdy)k
curl F=(RyQz)i+(PzRx)j+(QxPy)k
Given thath
F(x,y,z)=(x+yz)i+(y+xz)j+(z+xy)k
Now compute the required partial derivatives
P=x+yzPz=y and Py=z
Q=y+xzQz=x and Qx=z
R=z+xyRx=y and Ry=x
Substitute the partial derivatives
curl F=(RyQz)i+(PzRx)j+(QxPy)k
curl F=(xx)i+(yy)j+(zz)k=0

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