Chapter 9, Problem 10P

To determine

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

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 $F\left(x,y,z\right)=yk$ with equation (1),

$x=0$

$y=0$

$z=y$

The graph of vector field $F\left(x,y,z\right)=yk$ is shown below in Figure 1.

From Figure 1, it is noticed that all the vectors are in different direction and having different magnitude. All vectors are vertical. Some vectors are pointing upward to the xy-plane and some vectors are pointing downward to the xy-plane.

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