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Geometry: vector equation of a plane

  1. Mar 31, 2010 #1
    1. The problem statement, all variables and given/known data

    A plane contains non-collinear points A,B,C with position vectors a,b,c with respect to O. If s is the position vector of a point P, in the plane, with respect to O, show that it may be written as s = ua + vb + wc where u+v+w=1 (I think I have done this). If OP is perpendicular to the plane show

    u = n.(bxc)/|n|2

    v= n.(cxa)/|n|2

    w= n.(axb)/|n|2

    where n= bxc + cxa + axb, . is for the scalar product, x is for the vector product

    2. Relevant equations



    3. The attempt at a solution

    I have shown that n is normal to the plane. In an earlier part of the question I was asked to find u,v and w in terms of s,a,b,c. I found, for example, that u= [(b-c)x(s-c)]/[(b-c)x(a-c)], working from s= c + u(a-c) + v(b-c). I'm not even sure if this part is correct. Any advice on what to do would be great.
     
  2. jcsd
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