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Vector Perpendicular

  1. Jun 11, 2008 #1
    1. The problem statement, all variables and given/known data

    The equation for the line that goes through vector points A and B is

    i - 5j - 7k + t(9i + 15j + 12k)

    A is defined: i - 5j - 7k
    B is defined: 10i + 10j + 5k

    Find the position vector of point P such that OP is perpendicular to AB

    3. The attempt at a solution

    well a.b = 0 to be perpendicular

    but how does that help...

    Im lost

    Any ideas. My test is at 9am tomorrow (GMT). Can someone just explain the whole method for me.

  2. jcsd
  3. Jun 11, 2008 #2
    (9i + 15j + 12k) is your direction vector

    so you need <a,b,c> direction vector such that
    <a,b,c> . (9, 15, 12,) = 0

    pick any values for a,b,c

    so the line perpendicular is r = (0,0,0) + t <a,b,c>

    now, find intersection
  4. Jun 11, 2008 #3


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    Science Advisor
    Homework Helper

    Hi thomas49th! :smile:

    (btw, B isn't 10i + 10j + 5k, is it? :wink:)

    I assume P is to be on AB?

    ok, then OP must be i - 5j - 7k + t(9i + 15j + 12k)
    for some value of t.

    And, as you say, AB.OP = 0.

    So … ? :smile:

    I gotta go to bed now … :zzz:
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