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Math Help - vector parallel to intersection of planes

  1. #1
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    vector parallel to intersection of planes

    II need to find a vector parallel to the line of intersection between the plane 2x - y - 3z = 0 and the plane x + y + z = 1. I know I should know how to do this but my mind is drawing a complete blank!!!!! Thanks
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  2. #2
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    Please don't double post.

    Consider the cross product of the two normals of the plane.

    Their cross product will give the direction vector of the line of intersection. Any vector perpendicular to the normal of the first plane will lie in the first plane and any vector perpendicular to the normal of the second plane will lie in the second plane. Since the cross product of these two normals is perpendicular to both, it will lie in both planes, i.e. its line of intersection.
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