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Help me prove

  • Thread starter Reshma
  • Start date
  • #1
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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]
 

Answers and Replies

  • #2
TD
Homework Helper
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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]
 
  • #3
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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:

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