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

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Answer 1 · 2016-04-10T13:50:22

$sqrt67$

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

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,

$rarrd=sqrt((-1-2)^2+(4-(-3))^2+(-2-1)^2)$

$rarrd=sqrt((-3)^2+(4+3)^2+(-3)^2)$

$rarrd=sqrt((-3)^2+(7)^2+(-3)^2)$

$rarrd=sqrt(9+49+9)$

$color(green)(rArrd=sqrt67~~8.18$

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