# Thread: Vector planes and lines - finding their intersection

1. ## Vector planes and lines - finding their intersection

Let $
\prod _1
$
be a plane of equation x+y+2z=1,
$
\prod _2
$
the plane of equation -x+y=2, and
$
L_1
$
a line of equation $
\left( \begin{gathered}
0 \hfill \\
1 \hfill \\
1 \hfill \\
\end{gathered} \right) + t\left( \begin{gathered}
1 \hfill \\
0 \hfill \\
0 \hfill \\
\end{gathered} \right)

$

find $
\prod_1 \cap \,\prod _2
$
and $
\prod _1 \cap \,L_1

$

2. Originally Posted by mms
Let $
\prod _1
$
be a plane of equation x+y+2z=1,
$
\prod _2
$
the plane of equation -x+y=2, and
$
L_1
$
a line of equation $
\left( \begin{gathered}
0 \hfill \\
1 \hfill \\
1 \hfill \\
\end{gathered} \right) + t\left( \begin{gathered}
1 \hfill \\
0 \hfill \\
0 \hfill \\
\end{gathered} \right)

$

find $
\prod_1 \cap \,\prod _2
$
and $
\prod _1 \cap \,L_1

$
Start buy finding the equation of the line of intersection of the two planes. I assume you can do this.

Then the problem becomes finding the intersection of two lines, which I assume you can also do.

Please post your working and say where you get stuck if you need more help.