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Units Vectors and Planes

  1. Apr 4, 2007 #1
    1. The problem statement, all variables and given/known data

    Find 2 unit vectors u1, u2, lying in the plane, x-y+z=0, which are not parallel to each other.

    3. The attempt at a solution

    I've tried taking the unit vector of the normal vector <1,-1,1> which is <1/rad(3),-1/rad(3),1/rad(3)>, but my teacher has told me it is not in the plane.

    Then for my second vector, I created a parallel vector, but then I reread the question and found out they are not supposed to be parallel.
     
  2. jcsd
  3. Apr 4, 2007 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    Yes, obviously. x- y+ z= (1-(-1)+ 1)/rad(3)= rad(3) not 0! You are aware, I am sure, that the normal vector to a plane is not in the plane! (If you are not, reread the definition of "normal vector".)

    A very good case for always rereading the question (several times)! Yes, it says "not parallel".

    To find a vector in the plane x- y+ z= 0, look for values of x, y, z that satisfy that equation. There are, of course, an infinite number of such choices. You can choose any values you like for x and y, for example, and then solve the equation for z. 1 and 0 are good, simple, choices.
    If x= 1 and y= 0, then z must satisfy 1- 0+ z= 0.
    If x= 0 and y= 1, then z must satisfy 0- 1+ z= 0.

    Now form unit vectors from <x, y, z> and show that they are not parallel.
     
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