# What is the distance between (3, –1, 1)  and (–6, 3, 1) ?

Apr 21, 2018

color(maroon)("Distance between A & B " = vec(AB) = 9.85

#### Explanation:

$A \left({x}_{1} , {y}_{1} , {z}_{1}\right) = \left(3 , - 1 , 1\right) , B \left({x}_{2} , {y}_{2} , {z}_{2}\right) = \left(- 6 , 3 , 1\right)$

To find the distance between the two points A & B.

"Distance formula " color(blue)(d = sqrt((x_2-v_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2)

$d = \sqrt{{\left(- 6 - 3\right)}^{2} + {\left(3 + 1\right)}^{2} + {\left(1 - 1\right)}^{2}} = \sqrt{{9}^{2} + {4}^{2}}$

color(maroon)("Distance between A & B " = vec(AB) = 9.85