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Math Help - 3D vector question

  1. #1
    Newbie hymnseeker's Avatar
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    3D vector question

    The position vectors of the points A and B relative to an origin O are 5i + 4j + k, -i + j - 2k respectively. Find the position vector of the point P which lies on AB produced such that AP=2BP.
    My strategy was to calculate AB, then take 1/3 of this and add it to the position vector for B. However this returns the incorrect answer.

    Any ideas?
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  2. #2
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    Quote Originally Posted by hymnseeker View Post
    My strategy was to calculate AB, then take 1/3 of this and add it to the position vector for B.
    The equation \overrightarrow {AP}  = 2\overrightarrow {BP} \, \Rightarrow \,A - B - P that is B is between A&P.
    Your approach puts P between A&B.
    Try this \overrightarrow P  = 2\overrightarrow {AB} + \overrightarrow {A} . Does that work?
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  3. #3
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    Hello, hymnseeker!

    The position vectors of points A and B relative to an origin O
    are: . \vec A \:=\:\langle 5,4,1\rangle,\;\vec B \:=\:\langle -1,1,-2\rangle

    Find the position vector of point P which lies on AB produced so that: AP\:=\:2\!\cdot\!BP

    My strategy was to calculate AB, then take 1/3 of this ... .no
    Did you make a sketch?

    Code:
          : ← - - - - 2 - - - - → :
          *-----------*-----------*
          A           B ← - 1 - → P

    As you can see, B is the midpoint of AP.

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  4. #4
    Newbie hymnseeker's Avatar
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    I see...

    Thanks for your help Plato and Soroban, I understand now.
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