Question

Let the distance between the pairs of points whose cartesian coordinates are:
(i) $(-1,1,3),(0,5,6)$ be $\sqrt{k}$
(ii) $(2,3,-1),(2,6,2)$. be $3\sqrt{m}$
Find $\frac{k}{m}$ ?

Answer 1

Let $A=(-1,1,3)$ and $B=(0,5,6)$
Then application of distance formula gives us
$AB=\sqrt{1^2+4^2+3^2}=\sqrt{26}=\sqrt{k}$
Hence $k=26$.
Similarly
$C=(2,3,-1)$ and $C=(2,6,2)$. Then
$CD=\sqrt{0^2+3^2+3^2}=3\sqrt{2}=3\sqrt{m}$
Hence $m=2$.
Therefore $\frac{k}{m}=\frac{26}{2}=13$.