Question

Find the distances between the following pairs of points. (a) (5, −6, 12) and (0, 3, 13)

Answer 1

Hello !

Answer:

`\boxed{\sf d=√(107)\approx10.34 }`

Explanation:

The distance between two points A and B is given by the following formula:

`\sf AB=√((x_B-x_A)^2+(y_B-y_A)^2+(z_B-z_A)^2)`

Where
`\sf A(x_A,y_A,z_A)` and
`\sf B(x_B,y_B,z_B)`.

Given :

• A(5,-6,12)
• B(0,3,13)

Let's replace the coordinates with their values in the previous formula :

`\sf AB=√((0-5)^2+(3-(-6))^2+(13-12)^2)\\AB=√(25+81+1)\\\boxed{\sf AB=√(107)\approx10.34 }`

Have a nice day ;)