Chapter 10.1, Problem 35E

To determine

Tofind:The distance between the points $\left(1,0,-10\right)$ and $\left(0,-3,2\right)$ .

Answer to Problem 35E

The distance between the points $\left(1,0,-10\right)$ and $\left(0,-3,2\right)$ is $\sqrt{154}$ .

Explanation of Solution

Given information:

The points are $\left(1,0,-10\right)$ and $\left(0,-3,2\right)$ .

Calculation:

The points are $\left(1,0,-10\right)$ and $\left(0,-3,2\right)$ .

Use the distance formula for two points $\left(x_1,y_1,z_1\right)$ and $\left(x_2,y_2,z_2\right)$ .

  $\text{Distance}=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}$

Substitute $1$ , $0$ , $-10$ for $x_1$ , $y_1$ and $z_1$ respectively and $0$ , $-3$ , $2$ for $x_2$ , $y_2$ and $z_2$ respectively in the distance formula.

  $\begin{array}{c}\text{Distance}=\sqrt{{\left(0-1\right)}^2+{\left(-3-0\right)}^2+{\left(2-\left(-10\right)\right)}^2}\\ =\sqrt{{\left(-1\right)}^2+{\left(-3\right)}^2+{\left(12\right)}^2}\\ =\sqrt{1+9+144}\\ =\sqrt{154}\end{array}$

Therefore, the distance between the points $\left(1,0,-10\right)$ and $\left(0,-3,2\right)$ is $\sqrt{154}$ .