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Vector equation of line segment

  1. Jun 21, 2013 #1
    my text explains that a line segment is given by the equation r=(1-t)r0+tr1
    such that 0<=t<=1

    now i see how this formula is derived however i am not clear on why t must be between 0 and 1 if this is the equation for a line segment
     
  2. jcsd
  3. Jun 21, 2013 #2

    lurflurf

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    t is chosen in [0,1] so that ro and r1 are the endpoints. We can take t in [a,b] then we have
    r=(a+b-t)r0+tr1
    then the endpoints are
    br0+ar1
    ar0+br1
     
  4. Jun 21, 2013 #3
    if i were to derive this formula
    so we have

    vector r0 and vector r1 and want the equation of the line through the tip of r and r1 well in this case we can take the direction vector to be r1-r0 and replacing v with this in the equation r=r0+tv we have r=r0+t(r1-r0) and the we have r=r0(1-t)+tr1 this should work for any two vectors from the origin to the line why does the value of t need to be between 0 and 1
     
    Last edited: Jun 21, 2013
  5. Jun 21, 2013 #4

    lurflurf

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    It does not need to be between 0 and 1 it is just convenient we can have

    $$t \in [a,b] \\ \vec{r}=\vec{r_0}+\left( \frac{t-a}{b-a} \right) ^{192435341024} \vec{r_1}$$

    we can have the probability of getting heads when flipping a coin be 137.
    It is convenient to consider [0,1] so that the value equals the ratio.
    Nothing more nothing less.
     
  6. Jun 21, 2013 #5
    what if we are to choose a value of t that point outside of the segment how are we to know what values of t are contained within the segment
     
  7. Jun 21, 2013 #6
    Your question isn't clearly stated. If t is negative or greater than 1, then we are identifying a point on the extended line segment. So what is the question you want clarified?
     
  8. Jun 21, 2013 #7

    haruspex

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    Consider the distances from r = r0+t(r1-r0) to each of r0, r1. For r to be on the line segment, each distance must be <= |r1-r0|. What range does that give for t?
     
  9. Jun 21, 2013 #8
    ok this makes sense here we plug the the vectors into the equations and solve for t i see
     
  10. Jun 21, 2013 #9
    i have also posted another question about distance between lines
     
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