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Homework Help: 3d vectors. Does a point lie on the line?

  1. Feb 15, 2009 #1
    1. The problem statement, all variables and given/known data

    L1 has the vector equation r=2i+3j-5k + t(4i-2j+k)
    Does the point (16,-3,-2) lie on the line?

    2. Relevant equations


    3. The attempt at a solution

    I have a simple(i think) vector question but i just don't know the method to work it out.

    I have searched on the internet and through my books and i can't find a similar problem anywhere. Any help would be much appreciated.

  2. jcsd
  3. Feb 15, 2009 #2
    The point (16, -3, -2) can also be written as 16i - 3j - 2k. Does that help? Try writing the line in the similar form r = Ai + Bj + Ck where A, B, and C may be functions of t.
    Last edited: Feb 15, 2009
  4. Feb 15, 2009 #3


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    Science Advisor

    Conversely, the vector equation for the line r=2i+3j-5k + t(4i-2j+k) is the same as the parametric equation x= 2+ 4t, y= 3- 2t, z= -5+ k.
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