# vector parallel to intersection of planes

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• February 15th 2009, 11:14 AM
Frostking
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
• February 15th 2009, 03:27 PM
Pedro²
The normal vector of the first plane is $\overrightarrow n _1 = 2{\mathbf{i}} - {\mathbf{j}} - 3{\mathbf{k}}
$
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 $\overrightarrow n _1 \times \overrightarrow n _2$