The projection of a line segment on the coordinate axes are $2,3,6$. Then, the length of the line segment is

Let the length of the line segment be  $r$ and its direction cosines be $l,m,n$. Then, its projections on the coordinate axes are $lr, mr, nr$.

$\therefore$                              $lr=2$,$mr=3$ and $nr=6$

$\Rightarrow$              $l^2{r}^2+m^2{r}^2+n^2{r}^2=4+9+36$

$\Rightarrow$             $r^2\left(l^2+m^2+n^2\right)=49$

$\Rightarrow$             $r^2=49 \Rightarrow r=7$                $\left[\because l^2+m^2+n^2=1\right]$