Let $\mathbf { F } ( x , y , z ) = z \mathbf { i } + x \mathbf { j } + y \mathbf { k }$ . Find the divergence of F.
A) $- 2$
B)$- 1$
C)$0$
D)$1$
E)$2$
F)$3$
G)$4$
H)$5$

Question

Let $\mathbf { F } ( x , y , z ) = z \mathbf { i } + x \mathbf { j } + y \mathbf { k }$ . Find the divergence of F.
A) $- 2$ 
B)$- 1$ 
C)$0$ 
D)$1$
E)$2$
F)$3$
G)$4$
 H)$5$

Quizplus · Accepted Answer

The divergence of a vector field is the sum of the partial derivatives of its components. In this case, the divergence of F is:$$
abla \cdot \mathbf{F} = \frac{\partial}{\partial x} [z] + \frac{\partial}{\partial y} [x] + \frac{\partial}{\partial z} [y] = 0 + 0 + 1 = 1$$Therefore, the divergence of F is 1, which corresponds to choice C.

Let F(x,y,z)=zi+xj+yk\mathbf { F } ( x , y , z ) = z \mathbf { i } + x \mathbf { j } + y \mathbf { k }F(x,y,z)=zi+xj+yk

Let $\mathbf { F } ( x , y , z ) = z \mathbf { i } + x \mathbf { j } + y \mathbf { k }$