vecr=xhati+yhatj+zhatk হলে vec∇*vecr কত?

Explanation:

Another Explanation (5): প্রশ্ন: \( \vec{r} = x\hat{i} + y\hat{j} + z\hat{k} \) হলে \( \vec{\nabla} \cdot \vec{r} \) কত? 🤔 সমাধান: আমরা জানি, \( \vec{\nabla} = \frac{\partial}{\partial x}\hat{i} + \frac{\partial}{\partial y}\hat{j} + \frac{\partial}{\partial z}\hat{k} \) 🤓 তাহলে, \( \vec{\nabla} \cdot \vec{r} = \left( \frac{\partial}{\partial x}\hat{i} + \frac{\partial}{\partial y}\hat{j} + \frac{\partial}{\partial z}\hat{k} \right) \cdot \left( x\hat{i} + y\hat{j} + z\hat{k} \right) \) 🧐 ডট গুণনের নিয়ম অনুযায়ী, \( \vec{\nabla} \cdot \vec{r} = \frac{\partial}{\partial x}(x) + \frac{\partial}{\partial y}(y) + \frac{\partial}{\partial z}(z) \) 🤩 আমরা জানি, \( \frac{\partial}{\partial x}(x) = 1 \), \( \frac{\partial}{\partial y}(y) = 1 \) এবং \( \frac{\partial}{\partial z}(z) = 1 \) 🥳 সুতরাং, \( \vec{\nabla} \cdot \vec{r} = 1 + 1 + 1 = 3 \) 🎉 অতএব, \( \vec{\nabla} \cdot \vec{r} = 3 \) 😎