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Help me prove

  1. Aug 1, 2005 #1
    Let [itex]\vec A[/itex] be an arbitrary vector and let [itex]\hat n[/itex] be a unit vector in some fixed direction. Show that
    [tex]\vec A = (\vec A .\hat n)\hat n + (\hat n \times \vec A)\times \hat n.[/tex]
     
  2. jcsd
  3. Aug 1, 2005 #2

    TD

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    You can use the Vector Triple Product Identity on the last term:

    [tex]\left( {\vec A \times \vec B} \right) \times \vec C = - \vec A\left( {\vec B \cdot \vec C} \right) + \vec B\left( {\vec A \cdot \vec C} \right)[/tex]
     
  4. Aug 1, 2005 #3
    The vector [tex]\vec A[/tex] is expressed as the sum of its projections on [tex]W= \mathcal{L} (\hat{n})[/tex] and [tex]W^\bot[/tex].

    Prove that the two terms represent these.
     
    Last edited: Aug 1, 2005
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