L  be a line passing through P(9, 4, 4) and having d.r’s 1, -1, -2 meets the line  $\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2}$  at Q and the line  $\frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}$ at R then the length PQ+PR is 

P(9, 4, 4)
Q lie on  $\frac{x-1}{2}=\frac{y-3}{1}=\frac{z-2}{2}\Rightarrow Q=(2\lambda +1,\lambda +3,2\lambda +2)$
R lie on  $\frac{x-2}{1}=\frac{y-2}{2}=\frac{z-3}{3}\Rightarrow R=(\mu +2,2\mu +2,3\mu +3)$
Dr’s of QR=   $2\lambda -\mu -1,\lambda -2\mu +1,2\lambda -3\mu -1$
QR Parallel to L    $\Rightarrow \frac{2\lambda -\mu -1}{1}=\frac{\lambda -2\mu +1}{-1}=\frac{2\lambda -3\mu -1}{-2}\Rightarrow \lambda =\mu =3$
Q=(7, 6, 8) and R=(5, 8, 12)