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Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vectors ll

  1. Jun 2, 2012 #1
    1. The problem statement, all variables and given/known data

    Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vectors llACll= 2 llBCll

    2. Relevant equations

    Not sure.

    3. The attempt at a solution

    I found the equation of the line for vector AB:
    (1,2,-1) +t(2,0,1)

    Then found the scalar equation:
    x=1+2t
    y=-1
    x=2+t

    I found that t is 1/4 from knowing that C is 1/4 from llACll= 2 llBCll , (where the distance of C is 1/4 from B, and 3/4 from A).

    Plugging 1/4 = t gives
    x=3/2
    y=-1
    z=9/4

    I stopped here and did not bother plugging in 3/4 since the answer in the back of the book says:
    C(3,1,0) and C(5/3,-1/3,4/3)
     
  2. jcsd
  3. Jun 2, 2012 #2

    LCKurtz

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    Re: Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vector

    That isn't an equation since there is no = sign. And if you put (x,y,z)= on the left, it still isn't the correct equation for the line AB. (2,0,1) is point B, not the direction vector from A to B.
     
  4. Jun 3, 2012 #3
    Re: Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vector

    Okay, I re did it and obtained the direction vector AB which is (2,-1,-1).
    Using the same principle of t=1/4, I obtained (x,y,z) through the scalar equations, to be (3/2,-3/2,7/4).

    What did I do wrong?
     
  5. Jun 3, 2012 #4

    HallsofIvy

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    Re: Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vector

    The vector AB has length [itex]\sqrt{4+ 1+ 1}= \sqrt{6}[/itex]. Taking 1/4 of each coordinate gives an line segment of length [itex](1/4)\sqrt{6}[itex], not 1/4.
     
  6. Jun 3, 2012 #5

    SammyS

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    Re: Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vector

    Halls,

    You're missing a "/" in your final [/itex] tag.

    I put it into the above "QUOTE".

    (I will remove this post shortly, assuming you edit yours.) :smile:
     
  7. Jun 4, 2012 #6

    SammyS

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    Re: Find all points C on the line through A(1, -1, 2) and B(2, 0, 1) such that vector

    Well, I fell asleep & failed to remove it.

    DUH!
     
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