Arbitrary and unit vectors

  • Thread starter aigerimzh
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  • #1
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Homework Statement


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


Homework Equations





The Attempt at a Solution


I know that (A.n).n gives component of arbitrary vector, assume that it equals to Ax
 

Answers and Replies

  • #2
181
1

Homework Statement


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


Homework Equations





The Attempt at a Solution


I know that (A.n).n gives component of arbitrary vector, assume that it equals to Ax

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].
 
  • #3
HallsofIvy
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Again, you have used "*". What is that? The cross product? The usual notation is just "AX B".
 
  • #4
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Yes, here also I mean (Axn)xn
 
  • #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]?
 
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  • #6
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I think that (Axn)xn= aj?
 
  • #7
HallsofIvy
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I think that (Axn)xn= aj?
No. Try again. What is Axn first?
 

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