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Math Help - Line projection problem

  1. #1
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    Line projection problem

    Problem:

    The line x=1+t, y=1+2t, z=2-t is projected over the plane x-2y+3z-2=0, parallel with the vector a=(1,-1,0). Find the equation of the projected line.

    tnx
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    Denote

    \pi_1\equiv x-2y+3z=0

    and consider the plane

    \pi_2\equiv (x,y,z)=(1,1,2)+\alpha (1,2,-1)+\beta (1,-1,0)

    The solution is

    r\equiv \pi_1 \cap \pi_2

    Why?
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