Chapter 9.6, Problem 18AYU

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

$P_1=\left(-2,2,3\right)$ and $P_2=\left(4,0,-3\right)$

To determine

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

Answer to Problem 18AYU

Solution:

$2\sqrt{19}$

Explanation of Solution

Given:

$P_1 = (-2, 2, 3); P_2 = (4, 0, -3)$

Calculation:

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

$\begin{array}{lll}d\hfill & = \hfill & \sqrt{{(4 + 2)}^2 + {(0 - 2)}^2 + {(-3 - 3)}^2}\hfill \\ d\hfill & = \hfill & \sqrt{6^2 + {(-2)}^2 + {(-6)}^2}\hfill \\ d\hfill & = \hfill & \sqrt{36 + 4 + 36}\hfill \\ d\hfill & = \hfill & \sqrt{76}\hfill \\ d\hfill & = \hfill & 2\sqrt{19}\hfill \end{array}$