Answer
Skew
Work Step by Step
We will re-write the parametric equations as follows:
$x=1+2t; y=2+3t; z=3+4t$
and $t=\dfrac{x-1}{2}=\dfrac{y-2}{3}=\dfrac{z-3}{4}$
$x=-1+6s; y=3-s; z=-5+2s$
and $s=\dfrac{x+1}{6}=\dfrac{y-3}{-1}=\dfrac{z+5}{2}$
Now, we will set the equations equal to each other.
So, $s=\dfrac{2}{5}; t=-1+(3)(\dfrac{2}{5})=\dfrac{1}{5}$
Now, $3+(4) (\dfrac{1}{5})=-5+(2)(\dfrac{2}{5}) \implies \dfrac{19}{5} \ne -\dfrac{21}{5}$
This implies that the lines do not intersect, so they are skew.
