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Coordinate System

  1. Mar 4, 2009 #1
    For the transformation
    [itex]u_1=2x-y[/itex]
    [itex]u_2=x+2y[/itex]
    [itex]u_3=3z[/itex]

    verify that the [itex]u_i[/itex] form an orthogonal curvilinear coordinate system
     
  2. jcsd
  3. Mar 4, 2009 #2

    lanedance

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    any ideas? how do you show ui & uj are orthogonal when j does not equal i
     
  4. Mar 5, 2009 #3
    show dot product is 0.
    if [itex]u_1=(2x,-y,0),u_2=(x,2y,0)[/itex] then
    [itex]u_1 \cdot u_2 = 2x^2 -2y^2 \neq 0[/itex] though
     
  5. Mar 5, 2009 #4

    gabbagabbahey

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    Are you sure that the vectors aren't supposed to be:
    [tex]\vec{u_1}=2\hat{x}-\hat{y}[/tex]
    [tex]\vec{u_2}=\hat{x}+2\hat{y}[/tex]
    [tex]\vec{u_2}=3\hat{z}[/tex]

    .....there is a big difference between the scalar [itex]x[/itex] and the unit vector [tex]\hat{x}[/tex]!:wink:
     
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