1.1. Two lines $l$ and $m$ have equations $r=6i-2j+k+s(i+j-k)$  and $r=3i+3j-2k+t(3i-j+k)$ respectively.

Show that if the two lines intersect, then at the point of intersection the parameters $s$ and $t$ must satisfy the vector equation

         $(\begin{matrix}6+s\\-2+s\\1-s\end{matrix})=(\begin{matrix}3+3t\\3-t\\-2+t\end{matrix})$

1.2. Solve the simultaneous equations  $6+s=3+3t$ and  $-2+s=3-t,$  and show that the values found for $s$ and $t$do not also satisfy the equation $1-s=-2+t.$

1.3. What do the results of part (b) tell you about the lines $l$ and $m$?