Chapter 9.6, Problem 19AYU

In Problems 15-20, find the distance from $P_1$ to $P_2$.

$P_1=\left(4,-2,-2\right)$ and $P_2=\left(3,2,1\right)$

To determine

To find: The distance from $P_1$ to $P_2$.

Answer to Problem 19AYU

Solution:

$\sqrt{26}$

Explanation of Solution

Given:

$P_1 = (4, -2, -2);P_2 = (3, 2, 1)$

Calculation:

The distance from $P_1$ to $P_2$ is given by:

$\begin{array}{lll}d\hfill & = \hfill & \sqrt{{(3 - 4)}^2 + {(2 + 2)}^2 + {(1 + 2)}^2}\hfill \\ d\hfill & = \hfill & \sqrt{{(1-)}^2 + 16 + 9}\hfill \\ d\hfill & = \hfill & \sqrt{1 + 16 + 9}\hfill \\ d\hfill & = \hfill & \sqrt{26}\hfill \end{array}$