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

Apr 10, 2016

$\sqrt{67}$

#### Explanation:

color(blue)((2,-3,1)and(-1,4,-2)

Use the $3$ dimensional distance formula

color(brown)(d=sqrt((x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2)

So,

color(purple)(x_1=2,x_2=-1

color(purple)(y_1=-3,y_2=4

color(purple)(z_1=1,z_2=-2

Then,

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

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

$\rightarrow d = \sqrt{{\left(- 3\right)}^{2} + {\left(7\right)}^{2} + {\left(- 3\right)}^{2}}$

$\rightarrow d = \sqrt{9 + 49 + 9}$

color(green)(rArrd=sqrt67~~8.18