SOLUTION: Determine the intersection of lines r1=(2,-1,-1)+ t(1,2,-1)and r2=(-1,-1,1)+ u(-2,-1,1)

Algebra ->  Linear-equations -> SOLUTION: Determine the intersection of lines r1=(2,-1,-1)+ t(1,2,-1)and r2=(-1,-1,1)+ u(-2,-1,1)      Log On


   

Question 1153597: Determine the intersection of lines
r1=(2,-1,-1)+ t(1,2,-1)and
r2=(-1,-1,1)+ u(-2,-1,1)
Answer by AnlytcPhil(1806) About Me  (Show Source):
You can put this solution on YOUR website!


Equate x-coordinates:

2%2Bt=-1-2u
t%2B2u=-3

Equate y-coordinates

-1%2B2t=-1-u
2t%2Bu=0

Solve the system:

system%28t%2B2u=-3%2C2t%2Bu=0%29

Solution: (t,u) = (1,-2)  

Equate z-coordinates
 
-1-t=1%2Bu

See if that is consistent with (t,u) = (1,-2)
by substituting it:

-1-1=1%2B%28-2%29
-2=-1

No it's not consistent, so the lines do not intersect.

Edwin