Chapter 9, Problem 9P

To determine

To sketch: The vector field $F\left(x,y,z\right)=zj$.

Explanation of Solution

The vector field is a function of a space which gives a vector quantity at each point. It is a collection of arrows with a given magnitude and direction.

The general form of vector field in a space is given below,

$F\left(x,y,z\right)=xi+yj+zk$ (1)

Compare the vector field $F\left(x,y,z\right)=zj$ with equation (1),

$x=0$

$y=z$

$z=0$

The graph of vector field $F\left(x,y,z\right)=zj$ is shown below,

Figure 1

From Figure 1, it is noticed that all the vectors are in different direction and having different magnitude.

Thus, the Figure 1 shows the graph of the vector field $F\left(x,y,z\right)=zj$.