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Math Help - Finding the equation for a plane with only one point

  1. #1
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    Finding the equation for a plane with only one point

    How can I find the equation for a plane with a point T(1,1,-3), and we know that the surface normal for the plane is n = (4,2,1)

    I know how to find the equation for a plane with three points. But for this example I don't know how to even start.
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  2. #2
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    Let R=<x,y,z> then the plane is N\cdot (R-T)=0
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  3. #3
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    So if I understand it right...
    (4,2,1) * ((x,y,z) - (1,1,3)) = 0
    (4,2,1) * (x-1,y-1,x-3) = 0
    4x-4+2y-2+x-3=0
    4x+2y+x = 9
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  4. #4
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    Yes, that's right. I believe that if you stop and think about what you do when you are given three points, you will see that you use the three points to derive two vectors in the plane, then take the cross product of those to get a vector normal to the plane. Here you are given the normal vector so most of the work is already done!
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