Question

find the distance between the two points

$$\begin{gathered} P_1=(-1,2,-3) \\ {P}_2=(0,-2,1) \end{gathered}$$

Short answer

$d=\sqrt{33}$

Step-by-step solution

Step 1. The given information is 

$$\begin{gathered} P_1=(-1,2,-3) \\ {P}_2=(0,-2,1) \end{gathered}$$

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

$$\begin{gathered} d(P_1,P_2)=\sqrt{{(0-(-1\left)\right)}^2+{(-2-2)}^2+{(1-(-3\left)\right)}^2} \\ d(P_1,P_2)=\sqrt{1+16+16} \\ d(P_1,P_2)=\sqrt{33} \end{gathered}$$