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Math Help - Vector planes and lines - finding their intersection

  1. #1
    mms
    mms is offline
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    Vector planes and lines - finding their intersection

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

    find <br />
\prod_1 \cap \,\prod _2 <br />
and <br />
\prod _1 \cap \,L_1 <br /> <br />
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  2. #2
    Flow Master
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    Quote Originally Posted by mms View Post
    Let <br />
\prod _1 <br />
be a plane of equation x+y+2z=1,
    <br />
\prod _2 <br />
the plane of equation -x+y=2, and
    <br />
L_1 <br />
a line of equation <br />
\left( \begin{gathered}<br />
0 \hfill \\<br />
1 \hfill \\<br />
1 \hfill \\ <br />
\end{gathered} \right) + t\left( \begin{gathered}<br />
1 \hfill \\<br />
0 \hfill \\<br />
0 \hfill \\ <br />
\end{gathered} \right)<br /> <br />

    find <br />
\prod_1 \cap \,\prod _2 <br />
and <br />
\prod _1 \cap \,L_1 <br /> <br />
    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.
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