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Physics Vector Problem

  1. Aug 4, 2011 #1
    1. The problem statement, all variables and given/known data
    The vector r=xi+yj+zk, called the position vector, points from the origin(0,0,0) to an arbitrary point in space with coordinates(x,y,z).


    2. Relevant equations
    Use what you know about vectors to prove the following: All points (x,y,z) that satisfy the equation Ax+By+Cz=0 where A,B and C are constants,lie in a plane that passes through the origin and that is, perpendicular to the vector n=Ai+Bj+Ck.


    3. The attempt at a solution
    I can only show that the position vector pointing at (x,y,z) is perpendicular to n=Ai+Bj+Ck.. I did this by using cosa= (Ax+By+Cz)/rn to find the angle between n and r. Ax+By+Cz=0 so cosa=0 and a=90 degrees. But i can't still show that n is perpendicular to the plane. I'm also confused if the problem also asks to show that Ax+By+Cz=0 is a plane.Can somebody please help me. Thanks
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 4, 2011 #2
    Well, the plane is defined as [itex]\vec{r} \cdot \vec{n} = 0[/itex]. This states that r is perpendicular to n. So every point r for which this equation holds, lies in the plane. See also this page on planes: http://mathworld.wolfram.com/Plane.html. Hope this helps!
     
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