skew, intersecting, or parallel three-dimensional lines

[mathstresser]

Are the lines parallel, skew, or intersecting?

L1: (x-1)/(-4)=(y-2)/(2)=(z-3)/(-8)
L2: (x-1)/6=(y+4)/(-3)=(z+1)/12

I changed their forms...

L1:
x=1-4t
y=2+2t
z=3-8t

L2:
x=1+6t
y=-4-3t
z=-1+12t

The direction vector for L1 is <-4,2,-8> = <-2,1,-4>
The direction vector for L2 is <6,-3,12> = <2,-1,6>

So, they are not parallel. But how do I find if they are skew or intersecting?

 

[pka]

USE TWO DIFFERENT PARAMETERS.
L1:
x=1-4t
y=2+2t
z=3-8t

L2:
x=1+6s
y=-4-3s
z=-1+12s

Solve the system. See if there is a solution.
Be sure to check for consistently!.

 

[mathstresser]

I made a calculation error...

the direction vectors are
<-4,2,-8>=<-2,1,-4>
<6,-3,12>=<2,-1,4>

So... I would assume that they are parallel... But, I tried subustituting, like you said, and I can't get anything.... It's always -6=0 or 0=4, or something like that...

So, they don't intersect. Is that enough evidence to say they aren't skew (their opposite vectors)? and just say they are parallel?

 

[pka]

the direction vectors are
<-4,2,-8>=<-2,1,-4>
<6,-3,12>=<2,-1,4>
So... I would assume that they are parallel...

Yes they are parallel.