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Problem with vector operator

  1. Oct 18, 2013 #1
    Why do we use the coordinates of r in terms of x,y,z?Why dont we express coordinates of A in x,y,z?
     

    Attached Files:

  2. jcsd
  3. Oct 18, 2013 #2

    Simon Bridge

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    A is expressed in terms of x y and z.
     
  4. Oct 18, 2013 #3

    CompuChip

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    It's a matter of notation: we're just giving names to the three components of both vectors.
    You can replace them by ##r_1, r_2, r_3##, if that makes you feel any better. In general, if v is a vector, it is customary to denote its components by v1, v2, v3. However, if r is the position vector, then (x, y, z) is also quite common.

    Also note that though the fact that one is named r hints that it comes from a physical application in which a position vector is involved, the mathematical identity actually holds for any two vectors u, v.
     
  5. Oct 18, 2013 #4
    No its not..here at least
     
  6. Oct 18, 2013 #5
    If we use r1,r2,r3 then how would the vector operator operator operate on it?Like it didnt in A when we used A1,A2,A3.
     
  7. Oct 18, 2013 #6

    SteamKing

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    What are you talking about?
     
  8. Oct 18, 2013 #7

    Simon Bridge

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    I'm sorry - the example in your attachment very clearly states that

    A=A1i+A2j+A3k

    That means that
    - the x component of A is A1,
    - the y component of A is A2,
    - the z component of A is A3.

    Therefore: A is resolved in terms of x, y, and z.

    What did you think it meant?
     
  9. Oct 18, 2013 #8

    CompuChip

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    I don't understand your question, I think.

    If ##\mathbf v = v_1 \mathbf i + v_2 \mathbf j + v_3 \mathbf k## and ##\mathbf u = u_1 \mathbf i + u_2 \mathbf j + u_3 \mathbf k## then
    $$\mathbf u \times \mathbf v = (u_2 v_3 - u_3 v_2) \mathbf i + (u_3 v_1 - u_1 v_3) \mathbf j + (u_1 v_3 - u_3 v_1) \mathbf k$$

    That's just how the cross product works. It doesn't matter how you call the components. You could replace ##u_1##, ##u_2## and ##u_3## by ##x##, ##y## and ##z## or clubs, spades, hearts or bunny, cow, eagle and the definition would still be the same.

    Is it the notation of a vector like##\mathbf v = v_1 \mathbf i + v_2 \mathbf j + v_3 \mathbf k## instead of ##\mathbf v = (v_1, v_2, v_3)## that confuses you?
     
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