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

1. Jun 8, 2009

### hargun519

1. The problem statement, all variables and given/known data

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

2. Relevant equations

3. 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

2. Jun 8, 2009

### jeffreydk

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. $$\mathbf{n_1}\times\mathbf{n_2}=\langle 2,-1,-1\rangle \times \langle 1,2,3\rangle$$. 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.