যদি vecr=xhati+yhatj+2hatk হয় তবে vecnabla.vecr কত?

Explanation:

Another Explanation (5): দেওয়া আছে, \( \vec{r} = x\hat{i} + y\hat{j} + 2\hat{k} \) আমরা জানি, \( \vec{\nabla} = \frac{\partial}{\partial x}\hat{i} + \frac{\partial}{\partial y}\hat{j} + \frac{\partial}{\partial z}\hat{k} \) তাহলে, \( \vec{\nabla} \cdot \vec{r} = \left( \frac{\partial}{\partial x}\hat{i} + \frac{\partial}{\partial y}\hat{j} + \frac{\partial}{\partial z}\hat{k} \right) \cdot \left( x\hat{i} + y\hat{j} + 2\hat{k} \right) \) ডট গুণনের নিয়ম অনুসারে, \( \vec{\nabla} \cdot \vec{r} = \frac{\partial}{\partial x}(x) + \frac{\partial}{\partial y}(y) + \frac{\partial}{\partial z}(2) \) এখানে, \( \frac{\partial}{\partial x}(x) = 1 \), \( \frac{\partial}{\partial y}(y) = 1 \) এবং \( \frac{\partial}{\partial z}(2) = 0 \) সুতরাং, \( \vec{\nabla} \cdot \vec{r} = 1 + 1 + 0 = 2 \) অতএব, \( \vec{\nabla} \cdot \vec{r} = 2 \) 🥳