Question

If $A=\left(1,-2,-1\right),B=\left(4,0,-3\right),C=\left(1,2,-1\right)$ and $D=\left(2,-4,-5\right)$, find the distance between $AB$ and $CD$.

Answer 1

$A(1,-2,-1)B(4,0,-3)$

$C(1,2,-1)D(2,-4,-5)$

distance $AB=\sqrt{(1-4{)}^2+(-2-0{)}^2+(-1+3{)}^2}$

$=\sqrt{9+4+4}=\sqrt{17}$

$CD=\sqrt{(1-2{)}^2+(2+4{)}^2+(-1+5{)}^2}$

$=\sqrt{1+36+16}=\sqrt{93}$