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show that the vector F = (y+z)i +(z+x)j +(x+y)k is solenoidal
1 Answer
written 3.2 years ago by |
Given,
F = (y+z)i + (z+x)j + (x+y)k
To Prove :- F is solenoidal
Proof :-
F is solenoidal if ∇.F = 0
∴ F=(i∂∂x + j∂∂y + k∂∂z).[(y+z)i+(z+x)j+(x+y)k]
⟹F= ∂∂x(y+z) + ∂∂y(z+x) + ∂∂z(x+y)
⟹F= 0
$So,\ \therefore\ …