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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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    The normal vector of the first plane is \overrightarrow n _1  = 2{\mathbf{i}} - {\mathbf{j}} - 3{\mathbf{k}}<br />
and the second is \overrightarrow n _2  = {\mathbf{i}} + {\mathbf{j}} + {\mathbf{k}}, note that they are linearly independent. So a vector parallel to the line of intersection of them is given by \overrightarrow n _1  \times \overrightarrow n _2
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