Question

The divergence of \[ \left(2x^{2}z\,\hat{i}+xy^{2}z\,\hat{j}+3yz^{2}\,\hat{k}\right) \] at the point \((1,1,1)\) is

• A. \(-8\)
• B. \(0\)
• C. \(8\)
• D. \(12\)

Hint:

For \[ \vec{F}=P\hat{i}+Q\hat{j}+R\hat{k}, \] \[ \boxed{ \nabla\cdot\vec{F} = \frac{\partial P}{\partial x} + \frac{\partial Q}{\partial y} + \frac{\partial R}{\partial z}. } \]

Answer 1

The Correct Option is D