# Find equation of Line where Plane Meets

• Feb 25th 2011, 06:45 PM
heatly
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)
• Feb 25th 2011, 06:49 PM
Ackbeet
• Feb 25th 2011, 06:54 PM
heatly
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)
• Feb 25th 2011, 07:03 PM
Ackbeet
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?
• Feb 25th 2011, 07:08 PM
heatly
Thanks I just realised that mistake!
• Feb 26th 2011, 06:03 AM
Ackbeet
So what do you get now?
• Feb 26th 2011, 08:45 PM
heatly
I get:

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

Which is the published ans.
• Feb 28th 2011, 02:05 AM
Ackbeet
Jolly good.