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Work out the line equation (parametric equation)

  1. Apr 21, 2012 #1
    1. The problem statement, all variables and given/known data
    Let the point A and v1,v2,v3 non-coplanar vectors.
    Let the plane
    [tex]{\pi _1})P=A+{\lambda _1}{v_1}+{\lambda _2}{v_2}[/tex]

    Consider any vector u non-colinear with v3 and the plane:
    [tex]{\pi _2})P=A+{\lambda _3}{v_3}+{\lambda _4}u[/tex]

    2. Task
    Work out the equation of the line
    [tex]r={\pi _1}\cap {\pi _2}[/tex]

    3. The attempt at a solution
    No idea how to start. I just know that the point A belongs to both planes and the point A belongs to a line with the equation form of: [tex]A+\lambda v[/tex] but I don't know what to do next.

    Thanks!
     
  2. jcsd
  3. Apr 22, 2012 #2

    SammyS

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    Find a vector, n1, normal to plane π1, and a vector, n2, normal to plane π2.

    How is the line of intersection of the two planes oriented w.r.t. these two normal vectors, n1 and n2 ?
     
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