Question

lines

Answer 1

@Valpey @lgbasallote

Answer 2

Definitely not parallel as the signs are orthogonal.

Answer 3

since the coefficints of t are the component of the vector parallel to line so we have two vectors
v1=<3,1,-2>
v2=<2,-1,-1>

Answer 4

now check the ratio of the two vectors if the ratios of the components of the vectors are equal they will be Parallel.

\[\Large \frac{3}{2} \ne \frac{1}{-1} \ne \frac{-2}{-1}\]
so they are not parallel.

Answer 5

But how would I show they are intersecting?

Answer 6

like i understnad why they arent parallel but how about intersection

Answer 7

okay for this you have to solve the following
x=3t+1
y=t+1
z=-2t

now for second line use s instead of t
x=2s+3
y=-s
z=-s-1

set the both x and y components equal
3t+1=2s+3
t+1=-2s

solve these for t and s let me know what you get.

Answer 8

s= 0 t = -1/3

Answer 9

sorry try again ! i used t instead of s previously solve these two

3t+1=2s+3
t+1=-2s

Answer 10

arent those the same things?

Answer 11

If they intersect then for some t and s:
<1,1,0>+t<3,1,-2>=<3,0,-1>+s<2,-1,-1>
Which translates into three equations:
1+3t =3+2s
1+ t = -s
0- 2t =-1-s

Answer 12

Oh i see. Let me solve for them

Answer 13

s =-1 t = 0

Answer 14

i am committing typo mistakes again and again :(

here it is in detail
okay for this you have to solve the following
x=3t+1
y=t+1
z=-2t

now for second line use s instead of t
x=2s+3
y=-s
z=-s-1

set the both x and y components equal
3t+1=2s+3
t+1=-s
solving these two equations
t=0
s=-1
now set the z components equal and put the value of s and t
-2t=s-1
-2(0)=-1-1
\[\Large 0 \ne -2\]
so the lines are not intersecting!
these are skew lines

Answer 15

i said they were skew lines and that was wrong

Answer 16

@mukushla

Answer 17

s =-1 t = 0 is correct. The lines intersect at
<3*0+1,0+1,-2*0> =<1,1,0>
and <2*(-1)+3,-(-1),-(-1)-1>=<1,1,0>

Answer 18

@sami-21 you wrote -s-1 then you wrote s-1. Another typo, I suppose.

Answer 19

yes you are correct actually i made another typo
z component is
-2t=-s-1
-2(0)=-(-1)-1
0=0
so yes they intersects !!!

Answer 20

Oh i see thanks guys

Answer 21

Your proof should have ended:
now set the z components equal and put the value of s and t
-2t=-s-1
-2(0)=-(-1)-1=0