Chapter 9, Problem 26RE

To determine

To plot : The points and find the distance between them.

Explanation of Solution

Given: The points are $P\left(0,2,4\right)$ and $Q\left(1,3,0\right)$ .

The plot for the point $P$ and $Q$ is shown in figure below.

  

    Figure (1)

The plot for point $Q$ is shown in figure below.

  

    Figure (2)

The distance between the two points is calculated as,

  $\begin{array}{c}d\left(P,Q\right)=\sqrt{{\left(d-a\right)}^2+{\left(c-b\right)}^2+{\left(h-c\right)}^2}\\ =\sqrt{{\left(1-0\right)}^2+{\left(3-2\right)}^2+{\left(0-4\right)}^2}\\ =\sqrt{1+1+16}\\ =3\sqrt{2}\end{array}$

Therefore, the plot is shown in Figure (1), Figure (2) and the distance is $3\sqrt{2}\text{units}$ .