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Homework Help: Vector Help :yuck:

  1. Sep 26, 2004 #1
    Hi :smile:

    I need a reminder on how to do this vector stuff... Here's the problem, please help:

    (Planes)
    Find the angle between x+y+z=1 and x+2y+3z=6.

    So there are two planes, and I need to find the angle between the normals of these planes.

    Any hints will help. Thanks! :biggrin:

    Peace, Love, & Happiness,

    Monica :wink:
     
    Last edited: Sep 26, 2004
  2. jcsd
  3. Sep 26, 2004 #2
    bump :uhh:
     
  4. Sep 27, 2004 #3
    [tex]
    \begin{multline*}
    \begin{split}
    &For\ plane\ 1:\ x+y+z=1:\\
    &Choose\ any\ 3\ points\ on\ the\ plane \ to\ find\ 2\ vectors\ on\ the\ plane.\\
    &A(0,0,1);\ B(0,1,0);\ C(1,0,0)\\
    &\vec{a}=\hat{k};\ \vec{b}=\hat{j}; \ \vec{c}=\hat{i}\\
    &\vec{d}=\vec{b}-\vec{a}=\vec{j}-\hat{k}: The\ first\ vector\\
    &\vec{e}=\vec{c}-\vec{a}=\vec{i}-\hat{k}: The\ second\ vector\\
    &\vec{f}=\vec{d}\times\vec{e}=-\hat{i}-\hat{j}-\hat{k}: Normal\ vector\ to\ plane\ 1.\\

    &For\ plane\ 2:\ x+2y+3z=6:\\
    &Choose\ any\ 3\ points\ on\ the\ plane \ to\ find\ 2\ vectors\ on\ the\ plane.\\
    &G(0,0,2);\ H(6,0,0);\ M(0,3,0)\\
    &\vec{g}=2\hat{k};\ \vec{h}=6\hat{i}\; \ \vec{m}=3\hat{j}\\
    &\vec{n}=\vec{h}-\vec{g}=6\vec{i}-2\hat{k}: The\ first\ vector\\
    &\vec{p}=\vec{m}-\vec{g}=3\vec{j}-2\hat{k}: The\ second\ vector\\
    &\vec{q}=\vec{n}\times\vec{p}=6\hat{i}+12\hat{j}+18\hat{k}: Normal\ vector\ to\ plane\\
    &\vec{r}=\vec{q}/6=\hat{i}+2\hat{j}+3\hat{k}: Another\ normal\ vector\ to\ plane\\
    &\vec{f}\bullet \vec{r}=frcos\ \theta; \ \theta=158^0
    \end{split}
    \end{multline*}
    [/tex]
     
    Last edited: Sep 27, 2004
  5. Sep 27, 2004 #4
    Thanks! That helped a lot :)
     
  6. Sep 27, 2004 #5
    Or more generally: if a plane has the equation ax + by + cz + d = 0, then a normal vector to that plane is (a, b, c).
     
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