Chapter 9, Problem 15P

To determine

The graph of vector field $F\left(x,y,z\right)=i+2j+3k$.

Answer to Problem 15P

The graph of vector field $F\left(x,y,z\right)=i+2j+3k$ matches with the graph IV.

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 $F\left(x,y,z\right)=i+2j+3k$ with equation (1),

$x=1$

$y=2$

$z=3$

The graph of vector field $F\left(x,y,z\right)=i+2j+3k$ is shown below,

Figure (1)

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

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

Figure (2)

Thus, the graph of vector field $F\left(x,y,z\right)=i+2j+3k$ matches with the graph IV.