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A vectors problem

  1. Jun 27, 2012 #1
    1. The problem statement, all variables and given/known data

    X divides a line segment (AB) in a ratio of 3:4. Y divides line segment AX in a ratio of 1:2.
    If K is any point of the line containing A,B,X and Y; Please show that AY= 1/7OB - 1/7OA

    2. Relevant equations
    Not sure if any. Just adding and subtracting vectors.


    3. The attempt at a solution

    Alright so I know that 1/4 AB +BO would equal XO, but i don't know what do next. Thanks for the help.
     
  2. jcsd
  3. Jun 27, 2012 #2

    tiny-tim

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    hi manmachine! :smile:
    do you mean "If O is any point of the line containing A,B,X and Y; Please show that AY= 1/7OB - 1/7OA" ? :confused:

    hint: what is OB - OA ? :wink:
     
  4. Jun 27, 2012 #3
    This has nothing to do with the quesiton but how do i ask question on this forum?
     
  5. Jun 27, 2012 #4

    tiny-tim

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    welcome to pf!

    hi 106267! welcome to pf! :smile:
    here's something i've been drafting … (some of the opinions are my own)

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  6. Jun 27, 2012 #5
    It is AB? I don't know what to do next!
     
  7. Jun 27, 2012 #6

    tiny-tim

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    yes! :smile:

    ok, so now all you need to prove is AY = 1/7 AB :wink:
     
  8. Jun 27, 2012 #7
    And then what next?? I know, I know, I know I ask so many questions. Shame on me. Had surgery so couldn't come to many lectures.
     
  9. Jun 27, 2012 #8

    tiny-tim

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    write that in vector equations …

    what do you get? :smile:
     
  10. Jun 27, 2012 #9
    Ab= ax+ xy?
     
  11. Jun 27, 2012 #10

    tiny-tim

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    uhh? :confused:

    there's two equations

    try this one first …

    X divides a line segment (AB) in a ratio of 3:4​
     
  12. Jun 27, 2012 #11
    So AX+XB=AB?
     
  13. Jun 27, 2012 #12

    tiny-tim

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    well, yes, but that is true wherever X is, isn't it?

    you need an equation with 3 and 4 (or 7) in !!
     
  14. Jun 27, 2012 #13
    How can I do that? What is it? I am so bad at this :P
     
  15. Jun 27, 2012 #14

    HallsofIvy

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    First, in your original post you said "If K is any point of the line containing A,B,X and Y; Please show that AY= 1/7OB - 1/7OA" which makes no sense. tiny-tim, in his first response, asked if you meant "O" rather than "K" but you never answered. tiny-tim proceeded to assume you meant "O".

    Here's how I would do this problem. Let "A" be "0" on a number line. Since 3+ 4= 7, take "B" to be "7" on that same number line. That choice makes "X divides a line segment (AB) in a ratio of 3:4" easy: "X" is at the number "3" on that number line.- AX= 3 and XY= 4, a ratio of 3:4. And "Y divides line segment AX in a ratio of 1:2" is also easy: "Y" is at the number "1"- AY= 1 and YX= 2 so the ratio is 1:2.

    Let "O" be any point on that number line, at, say "z". Then OB is |z- 7| and OA is |z|. We have already seen that AY= 1. Do the algebra.
     
  16. Jun 27, 2012 #15

    tiny-tim

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    "X divides a line segment (AB) in a ratio of 3:4"​

    manmachine, what does that mean in ordinary english? :smile:
     
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