Let $\mathbf { r } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$ and $r = | \mathbf { r } |$.
Find $\nabla \cdot ( \mathbf { r } )$.
A) 5
B) 3
C) 1
D) 2
E) None of these

Question

Quizplus · Accepted Answer

We have $\mathbf{r} = x\mathbf{i} + y\mathbf{j} + z\mathbf{k}$, so $
abla \cdot \mathbf{r} = \frac{\partial}{\partial x}(x) + \frac{\partial}{\partial y}(y) + \frac{\partial}{\partial z}(z) = \boxed{3}$.

Let r=xi+yj+zk\mathbf { r } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }r=xi+yj+zk

Let $\mathbf { r } = x \mathbf { i } + y \mathbf { j } + z \mathbf { k }$