# What is the distance between  (–1, 2, –3)  and (–1, 4, –2) ?

Aug 14, 2016

$A = \left(- 1 , 2 , - 3\right) \text{ ; "A_x=-1" ; "A_y=2" ; } {A}_{z} = - 3$

$B = \left(- 1 , 4 , - 2\right) \text{ ; "B_x=-1" ; "B_y=4" ; } {B}_{z} = - 2$

$\Delta x = {B}_{x} - {A}_{x} = - 1 + 1 = 0$
$\Delta y = {B}_{y} - {A}_{y} = 4 - 2 = 2$
$\Delta z = {B}_{z} - {A}_{z} = - 2 + 3 = 1$

$\text{The distance between A and B can be calculated using }$

${s}_{\text{A,B}} = \sqrt{\Delta {x}^{2} + \Delta {y}^{2} + \Delta {z}^{2}}$

${s}_{\text{A,B}} = \sqrt{{0}^{2} + {2}^{2} + {1}^{2}}$

${s}_{\text{A,B}} = \sqrt{4 + 1}$

s_("A,B")=sqrt(0^2+2^2+1^2)=sqrt 5 " unit"