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show that the vector F = (y+z)i +(z+x)j +(x+y)k is solenoidal

topic : VECTOR CALCULUS

1 Answer
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Given,

F = (y+z)i + (z+x)j + (x+y)k


To Prove :- F is solenoidal


Proof :-

F is solenoidal if ∇.F = 0

 F=(ix + jy + kz).[(y+z)i+(z+x)j+(x+y)k]

F= x(y+z) + y(z+x) + z(x+y)

F= 0

$So,\ \therefore\ …

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