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Math Help - 2 dimensional plane in four dimensions

  1. #1
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    2 dimensional plane in four dimensions

    In R4 find the equation of the 2 dimensional plane that passes through the point (0,1,1,-2) and is normal to the vectors N = (2, -1, 0, 1) and M = (0, -1, 3, 0).

    I know that you can define a plane as (P-v).N = 0 and (P-v).M=0. What do I have to do in this case?
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  2. #2
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    Quote Originally Posted by TTim View Post
    In R4 find the equation of the 2 dimensional plane that passes through the point (0,1,1,-2) and is normal to the vectors N = (2, -1, 0, 1) and M = (0, -1, 3, 0).

    I know that you can define a plane as (P-v).N = 0 and (P-v).M=0. What do I have to do in this case?
    choose any point Q=(x,y,z,t) on the plane and let P=(0,1,1,-2). then \vec{PQ}=(x,y-1,z-1,t+2) and we want to have \vec{PQ} \cdot M=\vec{PQ} \cdot N= 0, which

    gives us: 2x-y+t+3=y-3z+2=0. thus y=3z-2, \ t=3z-2x-5. hence the vector equation of the 2-dimensional plane that you're looking for is:

    (0,-2,0,-5)+(1,0,0,-2)x + (0,3,1,3)z, where x,z are any real numbers.
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