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Vectors 3D product question!

  1. Sep 1, 2008 #1
    1. With respect to origin O, point A has position vector 30i - 3j - 5k. The line L passes through O and is parallel to the vector 4i - 5j -3k. The point B on L is such that AB is perpendicular to L. Find the length of AB. Find the position vector of B.

    3. The attempt at a solution
    Ok this is what i did.
    Let L=y(4i -5j -3k)
    Let b=x(4i -5j -3k)
    Hence AB = [(4x-30)i (-5x+3)j (-3x+5)k]

    Heres where i got quite stuck

    Since AB is perpendicular to L. I tried AB.L=0
    But i'm not very sure how do i solve this since there are 2 unknowns.

    Ahh! Please help me out here! Thanks!
  2. jcsd
  3. Sep 1, 2008 #2


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    Staff Emeritus
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    What is the equation of the plane containing A and having 4i- 5j- 3k as normal vector?

    Where does the line L intersect that plane? That is point B.
  4. Sep 1, 2008 #3
    Ahhh! Thanks! I missed out on the line that was on the next page of the book. :eek: Ok i can take it from here
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