Question

Let S be a piecewise smooth surface of the sphere x2 + y2 + z2 = 16, z> 0, bounded by a simple closed curve C. Let $\overrightarrow V= (3x-y)\hat{i}-2yz^2\hat{j}-2y^2z\hat{k}$ be a vector field which is continuous and has continuous first order partial derivatives in a domain which contains S. Then the value of $\int\int(\nabla\times\overrightarrow V).\hat{n}dA$, where $\hat{n}$ the unit normal vector to S is:

• A. $\frac{16}{3}$
• B. 48π-3
• C. 64+3π
• D. 16π

Answer 1

Answer: (D)

16π

Answer 2

The correct answer is(D): 16π