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Math Help - Vector Equations

  1. #1
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    Question Vector Equations

    i think this is simple, but it still confuses me at times

    say i have 2 position vectors:

    b = 2i - 3j
    c = 3i - 2j + sqrt(2)k

    i am asked to give the equation of the line going through these 2 points

    i know this equation is given by r=a + λb

    where a is the position vector of a point on the line
    (in this case it can be b or c)

    and b is the Direction Vector of the line, and this can be calculated easily by working out (c - b),

    BUT

    can the direction Vector also be calculated by working out (b - c)??

    Because in doing so the answer will be completely different, but i think that it would still qualify as an equation of a line passing through points b and c no?

    just wanted to clarify this, thanks in advance for any assistance
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  2. #2
    MHF Contributor
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    Yes you can because b-c and c-b are both direction vectors of the line

    The answer will not be so different : it is a matter of changing \lambda in -\lambda
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  3. #3
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    i assumed as much..

    still, how do you decide when to switch λ with -λ in the equation?

    i mean how do you decide which Direction Vector requires you to do so (b-c) or (c-b)?

    thanks again
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  4. #4
    MHF Contributor
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    You can write r = a + k(b-c) or r = a + k'(c-b)
    It does not matter
    The relationship between k and k' is k=-k'

    You can choose any direction vector to write r
    Last edited by running-gag; April 30th 2010 at 12:00 PM. Reason: Precision added
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