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Find the relation between x,y and z

  1. Aug 18, 2013 #1

    utkarshakash

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    1. The problem statement, all variables and given/known data
    The coplanar points A,B,C,D are (2-x, 2,2); (2,2-y,2); (2,2,2-z): (1,1,1)

    2. Relevant equations

    3. The attempt at a solution
    a(2-x, 2,2) + b(2,2-y,2) + c(2,2,2-z) = (1,1,1)

    Equating respective components

    ax=by=cz=k

    The answer is 1/x + 1/y + 1/z = 1 but in my case it does not satisfy this.
     
  2. jcsd
  3. Aug 18, 2013 #2
    Look here: http://mathworld.wolfram.com/Coplanar.html
     
  4. Aug 18, 2013 #3

    haruspex

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    True, but there is another constraint on a, b, c. If the three vectors on the left are not collinear then with arbitrary a, b and c you could generate any vector in the space, not just those in the desired plane.
    If you bring in that extra constraint, the result does follow.
     
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