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Math Help - Vector Product #2

  1. #1
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    Vector Product #2

    Find the equation of the plane which passes through the point (1,2,3) and contains the line of intersection of the planes 2x-y+z=4 and x+y+z=4.

    thank you.
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  2. #2
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    What ideas have you had so far?
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  3. #3
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    vector product the two planes?

     \begin{pmatrix}<br />
2\\ <br />
-1\\ <br />
1<br />
\end{pmatrix}\begin{pmatrix}<br />
1\\ <br />
1\\ <br />
1<br />
\end{pmatrix}
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  4. #4
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    Hmm. Well, in order to define a plane, you need a normal vector, and a point in the plane. You have the point. How could you get a normal vector?
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  5. #5
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    Dot Product (1,2,3) with  \begin{pmatrix}<br />
2\\ <br />
-1\\ <br />
1<br />
\end{pmatrix}

    ??
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  6. #6
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    You're guessing. You need to think geometrically here. You've got one point on the plane, and, given the equations you have, you could generate the equation for a line in the plane. But to write down the equation for a plane, you need a line normal, or perpendicular, to the plane. How can you get that line?
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  7. #7
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    solved it
    by following the example
    http://answers.yahoo.com/question/in...7131929AAStpWu
    Last edited by BabyMilo; March 4th 2011 at 10:11 AM.
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  8. #8
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    Ok, great!
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