Question

find the distance between the two points

$$\begin{gathered} P_1=(-2,2,3) \\ {P}_2=(4,0,-3) \end{gathered}$$

Short answer

$d=2\sqrt{19}$

Step-by-step solution

Step 1. The given information is

$$\begin{gathered} P_1=(-2,2,3) \\ {P}_2=(4,0,-3) \end{gathered}$$

Step 2. Using distance formula d(P1,P2)=(x2-x1)2+(y2-y1)2+(z2-z1)2

$$\begin{gathered} d(P_1,P_2)=\sqrt{{(4-(-2\left)\right)}^2+{(0-2)}^2+{(-3-3)}^2} \\ d(P_1,P_2)=\sqrt{6^2+2^2+{(-6)}^2} \\ d(P_1,P_2)=\sqrt{36+4+36} \\ d(P_1,P_2)=\sqrt{76} \\ d(P_1,P_2)=2\sqrt{19} \end{gathered}$$