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

$