Given a vector \(\vec u = \frac{1}{3}\left( { - {y^3}̂ i + {x^3}̂ j + {z^3}̂ k} \right)\)and n̂ as the unit normal vector to the surface of the hemisphere (x2 + y2 + z2 = 1; z ≥ 0), the value of integral \(\smallint \left( {\;\nabla \times u} \right) \bullet \hat n\;dS\) evaluated on the curved surface of the hemisphere S is

Given a vector \(\vec u = \frac{1}{3}\left( { - {y^3}̂ i + {x^3}̂ j

1.	Given a vector \(\vec u = \frac{1}{3}\left( { - {y^3}̂ i + {x^3}̂ j + {z^3}̂ k} \right)\)and n̂ as the unit normal vector to the surface of the hemisphere (x2 + y2 + z2 = 1; z ≥ 0), the value of integral \(\smallint \left( {\;\nabla \times u} \right) \bullet \hat n\;dS\) evaluated on the curved surface of the hemisphere S is
A.	– π/2
B.	π/3
C.	π/2
D.	π
Answer» D. π

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