Question

Distance between the points (2, 1, 2) and (5, 1, 6) is

Answer 1

To find the distance between two points in 3D space, we can use the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2}
\]

For the points \( (2, 1, 2) \) and \( (5, 1, 6) \):

- \( (x_1, y_1, z_1) = (2, 1, 2) \)
- \( (x_2, y_2, z_2) = (5, 1, 6) \)

Now, substituting the coordinates into the formula:

\[
d = \sqrt{(5 - 2)^2 + (1 - 1)^2 + (6 - 2)^2}
\]

Calculating each term:

\[
d = \sqrt{(3)^2 + (0)^2 + (4)^2}
\]
\[
= \sqrt{9 + 0 + 16}
\]
\[
= \sqrt{25}
\]
\[
= 5
\]

Thus, the distance between the points \( (2, 1, 2) \) and \( (5, 1, 6) \) is \( 5 \).