Chapter 11.1, Problem 35E

To determine

To find: The distance between the points.

Answer to Problem 35E

The distance between the points is $12\text{unit}$ .

Explanation of Solution

Given Information:

The given points are $\left(6,-9,1\right),\left(-2,-1,5\right)$

Concept used:

A three-dimensional coordinate system can be formed by passing a z -axis perpendicular to both the x -axis and the y -axis at the origin.

The distance between the points is calculated as,

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

The distance between the points is calculated as,

  $\begin{array}{c}d=\sqrt{{\left(x_2-x_1\right)}^2+{\left(y_2-y_1\right)}^2+{\left(z_2-z_1\right)}^2}\\ =\sqrt{{\left(-2-6\right)}^2+{\left(-1-\left(-9\right)\right)}^2+{\left(5-1\right)}^2}\\ =12\text{unit}\end{array}$

Thus, the distance between the points is $12\text{unit}$ .