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2 points

  1. Nov 26, 2007 #1
    1. The problem statement, all variables and given/known data

    Consider two points located at [tex] \bold{r}_1 [/tex] and [tex] \bold{r}_2 [/tex] separated by a distance [tex] r = |\bold{r}_1 - \bold{r}_2| [/tex]. Find a vector [tex] \bold{A} [/tex] from the origin to a point on the line between [tex] \bold{r}_1 [/tex] and [tex] \bold{r}_2 [/tex] at distance [tex] xr [/tex] from the point at [tex] \bold{r}_1 [/tex], where [tex] x [/tex] is some number.



    2. Relevant equations



    3. The attempt at a solution

    So would it be [tex] \frac{x}{\sqrt{2}}\bold{r}_1 + \frac{x}{\sqrt{2}}\bold{r}_2 [/tex]?
     
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  3. Nov 27, 2007 #2

    HallsofIvy

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    No, it wouldn't! For one thing, the two coefficients are the same. If x is not 1/2, then the point will not be equidistant from the two points so the equation should not be symmetric. Where did you get that [itex]\sqrt{2}[/itex]?
     
  4. Sep 6, 2008 #3
    I have this same question on my homework problem set. I got something completely different. It takes up a the entire width of a piece of notebook paper and is two lines tall. Can anyone solve this so I can check my answer?
     
  5. Sep 6, 2008 #4

    HallsofIvy

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    If x is just "some number", then, in general, the new point will not be between r1 and r2. If x is between 0 and 1, then it will be.

    Try (1-x)r1+ xr2

    Notice that if x= 0, that is just r1 itself, which "0r" from r1. If x= 1, that is just r2 which is distance "1r" from r2. Finally, if x= 1/2, that is (r1+ r2)/2, the midpoint.
     
  6. Sep 6, 2008 #5

    tiny-tim

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    Welcome to PF!

    Hi rkbgt! Welcome to PF! :smile:

    hmm … shouldn't take that long …

    if you show us how it begins, maybe we can help …

    Hint: what is the general expression for a point on the line through r1 and r2? :smile:
     
  7. Sep 6, 2008 #6
  8. Sep 6, 2008 #7

    tiny-tim

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  9. Sep 6, 2008 #8
    Could someone just give me a 30 second explanation on how to go about these problems. The thing is, I went to a pretty crappy high school that never taught anything about vectors, and this is for my freshman honors physics class. I read the chapter, but it doesn't go over stuff this complicated (which may really not be that complicated).

    What do you mean by OA = OX1 + X1A? Is O the origin? What's X1?

    Thanks
     
  10. Sep 6, 2008 #9

    tiny-tim

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    X1 is the point located at [tex]\bold{r}_1[/tex].

    This is vector addition … see http://en.wikipedia.org/wiki/Vector_addition#Vector_addition_and_subtraction :smile:
     
  11. Sep 6, 2008 #10
    All right it's not just me. I've asked sophomores and juniors who have gone through the same class I'm taking and they have no idea how to do it. It's taught by a new professor now who went to MIT. Maybe it's a trick question. Maybe it can't be done and he just wants to see us all squirm on our first problem set. I would say my answer is right but the problem is, it's a scalar, not a vector. I am completely lost for any other method of solving this.
     
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