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Math Help - [SOLVED] Planes and vectors please help

  1. #1
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    [SOLVED] Planes and vectors please help

    I need to find the equation of a plane which passes through P( 1, 2, 0) and which is perpendicular to the planes
    2x - 3y + 4z + 1 = 0
    and
    -x + 2y +4z + 7 = 0


    so far I've found the r.n=p form of the above known planes, and calculated that they do in fact intersect, angle of intersection is something like 1.24 rads
    what next? please help
    thank you
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  2. #2
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    is this right?
    Compute the vector cross product of <2, -3, 4> and <-1, 2, 4>. This gives you a vector that is perpendicular to both given planes. <-20, -12, 1>

    Let Q(x, y, z) be a point in the sought plane. Then vector PQ is perpendicular to <-20, -12, 1>, and so their dot product is zero:

    <-20, -12, 1> <x-1, y-2, z-0> = 0
    -20(x-1) - 12(y-2) + 1(z-0) = 0
    20(x-1) + 12(y-2) - z = 0
    20x + 12y - z = 44
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  3. #3
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    Absolutely!

    Nice work!

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