# Thread: Find equation of Line where Plane Meets

1. ## Find equation of Line where Plane Meets

Find the equations for the line of intersctions of the planes:

x+y+z=1
x+y=2

I worked it out to be r(t)=3i-j-k+t(i-j)

The ans says:
r(t)=2j-k+t(-i+j)

3. x+y+z=1
x+y=2
let x=t
t+y+z=1
y=1-t-z
solving for x we get
x=3+t
now solving for y we get
y=-1-t
now solving forz we get
z=-1
therefore r(t)=3i-j-k+t(i-j)

4. Hmm. There's something wrong with your method if x = t and x = 3 + t. That's impossible, isn't it? I would suggest row reducing your augmented matrix thus:

$\left[\begin{array}{rrr|r}
1 &1 &1 &1\\
1 &1 &0 &2
\end{array}\right]\to\dots$

You should get a one-parameter family of solutions. What do you get?

5. Thanks I just realised that mistake!

6. So what do you get now?

7. I get:

r(t)=2j-k+t(-i+j)

Which is the published ans.

8. Jolly good.