find the co-ordinates of the point of intersection of the lines whose equations are, $\displaystyle \frac{x}{1}= \frac{y}{3}=\frac{z}{2}\ and \ \frac{x-2}{1}=\frac{y-3}{4}=\frac{z-4}{2}$
Re-write the equations:
$\displaystyle \left|\begin{array}{l}x = t\\y=3t\\z=2t\end{array}\right.$ ..... and ..... $\displaystyle \left|\begin{array}{l}x=s+2\\y=4s+3\\z=2s+4\end{ar ray}\right.$
Solve the system of simultaneous equations for s, t:
$\displaystyle \left|\begin{array}{l}t=s+2\\3t=4s+3\\2t=2s+4 \end{array}\right.$
I've got: (s, t) = (3, 5)
Therefore the point of intersection is P(5, 15, 10)