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Math Help - Intersecting Lines in a Plane

  1. #1
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    Intersecting Lines in a Plane

    Equation of plane: r= (-3,5,6) + s[-1,1,2] + v[2,1,-3]. I need the equation of 2 intersecting lines that lie on this plane. I know I can use s[-1,1,2], but I need to find another vector that is perpendicular to s[-1,1,2]. How can I find the intersecting vector?
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  2. #2
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    Quote Originally Posted by square View Post
    Equation of plane: r= (-3,5,6) + s[-1,1,2] + v[2,1,-3]. I need the equation of 2 intersecting lines that lie on this plane. I know I can use s[-1,1,2], but I need to find another vector that is perpendicular to s[-1,1,2]. How can I find the intersecting vector?
    The vector you are looking for is

    \vec v = (-1,1,2) \times \underbrace{\left((-1,1,2) \times (2,1,-3)  \right)}_{\text{normal to plane}} = (-5,-1,4)
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