Let S be a piecewise smooth surface of the sphere x 2 + y 2 + z 2 = 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:

Question

Let S be a piecewise smooth surface of the sphere x 2 + y 2 + z 2 = 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:

cdquestions Admin · Accepted Answer

The correct answer is(D): 16&pi;

Answer

$\frac{16}{3}$

Answer

Answer

Answer

The Correct Option is D

Solution and Explanation

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