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Arbitrary and unit vectors

  1. Sep 11, 2011 #1
    1. The problem statement, all variables and given/known data
    Let A be an arbitrary vector and let n be a unit vector in some fixed direction. Show that A=(A.n).n+(A*n)*n


    2. Relevant equations



    3. The attempt at a solution
    I know that (A.n).n gives component of arbitrary vector, assume that it equals to Ax
     
  2. jcsd
  3. Sep 11, 2011 #2
    Most straightforward way is to write out the Cartesian components and verify. Just keep in mind that [itex]n_x^2 + n_y^2 + n_z^2 = 1[/itex].
     
  4. Sep 11, 2011 #3

    HallsofIvy

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    Again, you have used "*". What is that? The cross product? The usual notation is just "AX B".
     
  5. Sep 11, 2011 #4
    Yes, here also I mean (Axn)xn
     
  6. Sep 11, 2011 #5

    HallsofIvy

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    You can set up you own coordinate system and so, without loss of generality, take n to be [itex]\vec{i}[/itex]. Write A as [itex]a\vec{i}+ b\vec{j}+ c\vec{c}[/itex].

    Then [itex]A\cdot n= a[/itex] so that [itex](A\cdot n)= a\vec{i}[/itex]. What are [itex]A\times n[/itex] and [itex](A\times n)\times n[/itex]?
     
    Last edited: Sep 11, 2011
  7. Sep 11, 2011 #6
    I think that (Axn)xn= aj?
     
  8. Sep 11, 2011 #7

    HallsofIvy

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    No. Try again. What is Axn first?
     
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