Chapter 9, Problem 16P

To determine

The graph of vector field $F\left(x,y,z\right)=i+2j+zk$.

Answer to Problem 16P

The graph of vector field $F\left(x,y,z\right)=i+2j+zk$ matches with the graph I.

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 $F\left(x,y,z\right)=i+2j+zk$ with equation (1).

$x=1$

$y=2$

$z=z$

The graph of vector field $F\left(x,y,z\right)=i+2j+zk$ is shown below,

Figure (1)

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

The Figure (1) and the above description match with the graph I.

Figure (2)

Thus, the graph of vector field $F\left(x,y,z\right)=i+2j+zk$ matches with the graph I.