vecV=x^2hati-2zhatj+yhatk হলে,div  vecV=? 

Explanation:

Another Explanation (5): দেওয়া আছে, \( \vec{V} = x^2 \hat{i} - 2z \hat{j} + y \hat{k} \) \( div \vec{V} \) নির্ণয় করতে হবে। আমরা জানি, \( div \vec{V} = \nabla \cdot \vec{V} \) এখানে, \( \nabla = \frac{\partial}{\partial x} \hat{i} + \frac{\partial}{\partial y} \hat{j} + \frac{\partial}{\partial z} \hat{k} \) সুতরাং, \( div \vec{V} = \left( \frac{\partial}{\partial x} \hat{i} + \frac{\partial}{\partial y} \hat{j} + \frac{\partial}{\partial z} \hat{k} \right) \cdot \left( x^2 \hat{i} - 2z \hat{j} + y \hat{k} \right) \) \( = \frac{\partial}{\partial x} (x^2) + \frac{\partial}{\partial y} (-2z) + \frac{\partial}{\partial z} (y) \) \( = 2x + 0 + 0 \) \( = 2x \) অতএব, \( div \vec{V} = 2x \) 🎉