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Math Help - Proving this Parametric Equation of a Line

  1. #1
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    Proving this Parametric Equation of a Line

    Hi,

    I`m having trouble proving these statements involving a linear equation:

    In R_n, given x = a + t*(b-a) where t is an element of [0,1] prove that:

    Selecting any two values t1 and t2, the vectors connecting the two points are parallel.

    The Line segment does not extend beyond points a and b.

    Thanks a lot!
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  2. #2
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    Re: Proving this Parametric Equation of a Line

    Quote Originally Posted by AKTilted View Post
    proving these statements involving a linear equation:
    In R_n, given x = a + t*(b-a) where t is an element of [0,1] prove that:
    Selecting any two values t1 and t2, the vectors connecting the two points are parallel.
    The Line segment does not extend beyond points a and b.
    Does this make sense to you?
    If \alpha\beta>0 then \alpha\vec{a}+\beta\vec{b} is a multiple of \vec{a}+\vec{b}.

    If so then note that \vec{a}+t_1(\vec{b}-\vec{a})=(1-t_1)\vec{a}+t_1\vec{b}
    Likewise \vec{a}+t_2(\vec{b}-\vec{a})=(1-t_2)\vec{a}+t_2\vec{b}

    So?

    P.S. As stated it may be false if t_1\cdot t_2=0
    Last edited by Plato; September 29th 2011 at 02:52 PM.
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