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Thread: point of intersection

  1. #1 point of intersection 
    Moderator Moderator AlexP's Avatar
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    Yes, this is a homework problem. I've included everything that I did. I got to the end, and I'm just off by a little bit. Probably just made a random little mistake somewhere that I can't catch.

    Find the point of intersection of the line through and and the plane given by .

    Here's what I've got...



    Parametric equations of the line:

    I substituted the parametric equations of the line into the equation of the plane...



    Combining like terms I got and solved it to obtain

    From here I substituted in the result...





    Plugging these back into the equation for the plane, I obtained 1, not 2, and this is where my problem lies. I'm probably missing something obvious, so help would be much appreciated...


    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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  3. #2 Re: point of intersection 
    . DrRocket's Avatar
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    Quote Originally Posted by Chemboy
    Yes, this is a homework problem. I've included everything that I did. I got to the end, and I'm just off by a little bit. Probably just made a random little mistake somewhere that I can't catch.

    Find the point of intersection of the line through and and the plane given by .

    Here's what I've got...



    Parametric equations of the line:

    I substituted the parametric equations of the line into the equation of the plane...



    Combining like terms I got and solved it to obtain

    From here I substituted in the result...





    Plugging these back into the equation for the plane, I obtained 1, not 2, and this is where my problem lies. I'm probably missing something obvious, so help would be much appreciated...
    You did everything right except the calculation following the final substitution. If you use the relations that you found for X, y and Z you get




    Then x-y+z=2 as required.


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  4. #3  
    Moderator Moderator AlexP's Avatar
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    Haha. I knew it would be something like that...forgot to add a 1. I'm so smart. Thank you.
    "There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges
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