anonymous
  • anonymous
Find the intersection point between two lines: L1=<-3,5,7>k+<1,-2,-0> L2=<3,-1,-4>t+<1,2,3>
Mathematics
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anonymous
  • anonymous
Find the intersection point between two lines: L1=<-3,5,7>k+<1,-2,-0> L2=<3,-1,-4>t+<1,2,3>
Mathematics
chestercat
  • chestercat
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experimentX
  • experimentX
just equate the values of x, y, z from those two lines and find the valeus of k and t. if you don't find singular values ... then they do not intersect.
anonymous
  • anonymous
Hey @experimentX . I tried solving this intersection using a similar method you showed me for the line and plane intersection, does it work here as well?
anonymous
  • anonymous
Yeah, I found the intersection using the x,y,z components from L1 and L2 and found the correct intersection. I was just wondering if we could solve it using the other way you showed me for the line and plane problem

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experimentX
  • experimentX
yeah it works .... just try to find the value of k and t ... from first two equation. put the value on the last equation. If it's invalid then the line does not intersect.
anonymous
  • anonymous
Okay, so far I have from L2: 1+3t -->k1 2-t ---->k2 3-4t--->k3 and L1: -3k1+5k2+7k3=1 Filling those values from L2 into L1, I get: 1=-3(1+3t)+5(2-t)+7(3-4t) 1=-3-9t+10-5t+21-28t t=27/42
experimentX
  • experimentX
lol ... what are you doing?? |dw:1350576239788:dw|
anonymous
  • anonymous
Was what I did not the way i'm suppose to do it? lol
anonymous
  • anonymous
I just tried to do it a similar way to the way we solved the line and plane intersection; breaking up the line equation into it's x,y,z components, then filling them into the plane equation, except here there's two lines, so I broke up one of the line equations into it's x,y,z, and filled it into the other line equation
experimentX
  • experimentX
you are making it complicated... we are trying to find the point common to both lines. so just equate x, y and z of both lines.
anonymous
  • anonymous
Got it, thanks :D
experimentX
  • experimentX
well ... trying to find a plane that would contain both lines is not bad either. good pratice for other problems!

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