Answer:
skew lines
Step-by-step explanation:
Given are two lines in 3 dimension as
[tex]L1: x=23+6t, y=12+3t, z=19+5t\\L2: x=-9+7t, y=-7+5t, z=-12+8t[/tex]
To find out whether parallel or skew or intersect
If parallel direction ratios should be proportional
Direction ratios of I line are 6,3,5 and not proportional to that of II line (7,5,8)
So not parallel
If intersect we must have same point for the two lines
Let us change parameter for II line to s to avoid confusion. If intersecting, then
[tex]23+6t = -9+7s\\12+3t = -7+5s\\19+5t =12+8s\\[/tex]
6t-7s=-32 and 3t-5s = -19
Solving
t=-3 and s =2
Check this with III equation
Left side = 19-15 =4 and right side = 12+16 =28
not equal
So there cannot be any point of intersection.
These two are skew lines
