অবস্থান ভেক্টর vecr=xhati+yhatj+zhatk হলে, vecnabla.vecr- 

Explanation:

Another Explanation (5): অবস্থান ভেক্টর \(\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}\)। এখানে, ডাইভারজেন্স অপারেটর \( \vec{\nabla} = \frac{\partial}{\partial x}\hat{i} + \frac{\partial}{\partial y}\hat{j} + \frac{\partial}{\partial z}\hat{k} \) 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, \(\vec{\nabla} \cdot \vec{r} = \frac{\partial x}{\partial x} + \frac{\partial y}{\partial y} + \frac{\partial z}{\partial z}\) যেহেতু, \(\frac{\partial x}{\partial x} = 1\), \(\frac{\partial y}{\partial y} = 1\) এবং \(\frac{\partial z}{\partial z} = 1\) সুতরাং, \(\vec{\nabla} \cdot \vec{r} = 1 + 1 + 1 = 3\) 🎉 অতএব, উত্তর: 3