Question

Find the distance from$P_1=\left(1,3,-2\right)to{P}_2=\left(4,-2,1\right).$

Short answer

The distance from $P_{1}to{P}_2$is$\sqrt{43}.$

Step-by-step solution

Step 1. Given Information

The given two points are $P_1=\left(1,3,-2\right)$and $P_2=\left(4,-2,1\right).$

Step 2. Finding the distance

To find the distance from $P_{1}to{P}_2$, use the distance formula which is $d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$

So,

$$\begin{gathered} d=\sqrt{{\left(4-1\right)}^2+{\left(-2-3\right)}^2+{\left(1-\left(-2\right)\right)}^2} \\ d=\sqrt{9+25+9} \\ d=\sqrt{43} \end{gathered}$$