1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Vector Help :yuck:
  1. Vectors help! (Replies: 13)

  2. Vectors help! (Replies: 2)

  3. Vectors Help (Replies: 12)

  4. Vectors Help (Replies: 12)

  5. Help with vectors? (Replies: 5)

Loading...