Answer:
The lines ared skew
Step-by-step explanation:
First we check if they are parallel. To do this we compare the ratios of the slopes of each component, and this should be the same:
[tex]\frac{L1_{x} }{L2_{x} } =\frac{L1_{y} }{L2_{y} }= \frac{L1_{z} }{L2_{z} }[/tex]
[tex]\frac{-2}{-1} =\frac{4}{3} =\frac{8}{2}[/tex]
As we can see the ratios are different so they are not parallel lines.
Now we test for intersesction:
we have to equate each component and solve it as a system:
From equation 1: u=2t-4 we replace this in eq. 2
From equation 2: t=1/2 replacing both in equation 3 should give us an identity
From equation 3: we reach 1=3 as this is not true, out hypothesis that the lines intersect is wrong.
Since this lines are not paralel and don't intersect we must conclude that the are skew
