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Homework Help: Does this line lie in this plane?

  1. Sep 20, 2010 #1
    1. The problem statement, all variables and given/known data
    See figure for problem statement. It asks if a given line lies in a given plane.


    2. Relevant equations



    3. The attempt at a solution

    Okay so first I translated the line into its parametric equations and then I subbed those into the equation of the plane respectively.

    After simplifying you'll find that,

    [tex]9t-1 = -1[/tex]

    Now my solutions manual states the following,

    *NOTE* There is no symbol for not-equivalent in tex, so I'm writing NE

    [tex]9t -1 NE -1[/tex]

    Why is this so?

    Why not let t = 0, and then -1 = -1 and then all will be well in world, no?

    What am I missing?
     

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  3. Sep 20, 2010 #2

    gabbagabbahey

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    \neq works :wink:

    Each value of [itex]t[/itex] corresponds to a single point on the line. If the entire line were to lie in the plane, the equation would have to be true for all values of [itex]t[/itex] (all points on the line), not just [itex]t=0[/itex]
     
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