Find the equation of the line of intersection of the planes:

  • Thread starter hargun519
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Homework Statement



2x-y-z=3 and x+2y+3z=7

Homework Equations





The Attempt at a Solution



Im stumped on this problem because initially i thought all i had to do was make z, or another variable zero and then just solve. However, it then turns into a nasty problem. Most of the examples in my book, for one of the equations there are 2 variables instead of 3. Hence to make the substitution easier. So, my question is how would i start the problem then?

Any help will be appreciated
 

Answers and Replies

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There are two parts two a problem like this. First you'll want to find the direction of the line of intersection, which is nothing but the cross product of the normal vectors of the planes, i.e. [tex]\mathbf{n_1}\times\mathbf{n_2}=\langle 2,-1,-1\rangle \times \langle 1,2,3\rangle[/tex]. Then all you need now to find the representation of the line is a point on that line right? So simply find an (x,y,z) value that satisfies both plane equations.
 

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