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:
![\frac{L1_{x} }{L2_{x} } =\frac{L1_{y} }{L2_{y} }= \frac{L1_{z} }{L2_{z} }](https://tex.z-dn.net/?f=%5Cfrac%7BL1_%7Bx%7D%20%7D%7BL2_%7Bx%7D%20%7D%20%3D%5Cfrac%7BL1_%7By%7D%20%7D%7BL2_%7By%7D%20%7D%3D%20%20%5Cfrac%7BL1_%7Bz%7D%20%7D%7BL2_%7Bz%7D%20%7D)
![\frac{-2}{-1} =\frac{4}{3} =\frac{8}{2}](https://tex.z-dn.net/?f=%5Cfrac%7B-2%7D%7B-1%7D%20%3D%5Cfrac%7B4%7D%7B3%7D%20%3D%5Cfrac%7B8%7D%7B2%7D)
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:
- 3-2t=-1-u
- 7+4t=18+3u
- -3+8t=7+2u
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