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 $I, m, n.$ Then, its projections on the coordinate axes are $Ir, mr, nr$

$\therefore lr=2,mr=3$ and $nr=6$

$\begin{array}{l}\Rightarrow l^2{r}^2+m^2{r}^2+n^2{r}^2=4+9+36\\ \Rightarrow r^2\left(l^2+m^2+n^2\right)=49\\ \Rightarrow r^2=49\Rightarrow r=7\end{array}$  $\left[\because l^2+m^2+n^2=1\right]$