Question

In Exercises 19-22, find the distance between the points. \((0,0,0), \quad(5,2,6)\)

Short answer

The distance between the points is \(\sqrt{65}\) units.

Step-by-step solution

Identify the coordinates

Given are two points with coordinates (0,0,0) and (5,2,6). The coordinates of the first point are (x1, y1, z1) = (0,0,0) and the coordinates of the second point are (x2, y2, z2) = (5,2,6).

Apply the distance formula

The formula for the distance between two points in three-dimensional space is: \[d = \sqrt{(x2-x1)^2 + (y2-y1)^2 + (z2-z1)^2}\]

Substitute in the values and calculate

Substitute the identified coordinates into the formula: \[d = \sqrt{(5-0)^2 + (2-0)^2 + (6-0)^2} = \sqrt{25 + 4 + 36} = \sqrt{65}\]