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

[hargun519]

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

 

[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.