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Math Help - 3d vector

  1. #1
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    3d vector

    Question: The position vectors of the points A, B and C referred to an origin O are 4i-3j-k and -8i+6j+5k respectively. If AB meets the z-axis at P, find the ratio AP:PB.

    What is mean by "If AB meets the z-axis at P" ?
    Can anyone explain to me please?
    And how do I solve it?

    Please help, thanks.
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  2. #2
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    Re: 3d vector

    Quote Originally Posted by alexander9408 View Post
    Question: The position vectors of the points A, B and C referred to an origin O are 4i-3j-k and -8i+6j+5k respectively. If AB meets the z-axis at P, find the ratio AP:PB.

    What is mean by "If AB meets the z-axis at P" ?
    Can anyone explain to me please?
    And how do I solve it?

    Please help, thanks.
    1. Stationary vector of C ( \vec c) is missing.

    2. AB is a straight line passing through A and B:

    AB: r = \langle 4,-3,-1 \rangle + t \cdot \langle 12, -9 ,-6 \rangle

    If this line has a common point with the z-axis the point P has the coordinates P(0,0,p)

    Determine p.

    3. When you finally have found P(0,0,1) calculate the distances |\overline{AP}| and |\overline{BP}| and determine the ratio of the distances. I've got \frac{|\overline{AP}|}{|\overline{BP}|} = \frac12
    Thanks from HallsofIvy and alexander9408
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