9000101005

Find the value of the real parameter $m$ which ensures that the lines $p$ and $q$ are intersecting lines (with a unique common point). $$\begin{array}{rlr}p:x& =1+t,& \\ y& =2-t,\\ z& =1-t;t\in \mathbb{R}\end{array}\begin{array}{rlr}q:x& =s,& \\ y& =1+s,\\ z& =3+ms;s\in \mathbb{R}\end{array}$$