Did I do it right?

Question

Given lines
L1.....x=2-2t , y=1+t , z=1+2t
L2.....x=2s ,y=2-s , z= 1-s

Determine whether lines are parallel, intersecting or skew.

Solution:
D1<-2,1,2> , D2<2,-1,-1> therefore skew lines

Should I take the ration to to determine which state.

Answer 1

Since the direction vectors are not multiples of each other, we know the lines aren't parallel. But you can't tell from the direction vectors alone whether they intersect or not; you have to solve the equations.
2s = 2 - 2t
2 - s = 1 + t
1 - s = 1 + 2t
<=>
s + t = 1
s + t = 1
s + 2t = 0
<=> t = -1, s = 2
Since there is a single solution, the lines intersect.

Answer 2

yes

Answer 3

yea u got it