# Thread: Vector planes and lines - finding their intersection

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

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

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

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

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