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Forces Vectors And Dot Products

  1. Nov 20, 2009 #1
    Hello all :smile:,

    I am interested in the following problem:

    In an ensemble of atoms, the forces on atom A and atom B are given by the vectors Fa=Fax+Fay+Faz and Fb=Fbx+Fby+Fbz, respectively.

    There respective positions are given by,

    Pa=Pax+Pay+Paz and Pb=Pbx+Pby+Pbz

    I have two questions:

    (1) Would I be right in thinking that the dot product of Fa and Pb will give the magnitude of the force on atom A in the direction of atom B?

    (2) Also, is the dot product of Fa and Fb the attractive force between the atoms?

    Any help would be greatly appreciated :smile::smile:!!

    Ewan.
     
  2. jcsd
  3. Nov 22, 2009 #2

    LCKurtz

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    If they are vectors, use vector notation. Your notation doesn't make any sense.
    [tex]\vec F_a = \langle a_1,a_2,a_3\rangle,\ \vec F_b = \langle b_1,b_2,b_3\rangle[/tex]

    [tex]\vec P_a = \langle p_1,p_2,p_3\rangle,\ \vec P_b = \langle q_1,q_2,q_3\rangle[/tex]

    I have two questions:

    (1) Would I be right in thinking that the dot product of Fa and Pb will give the magnitude of the force on atom A in the direction of atom B?
    [/quote]

    No. The direction from atom A to atom B would be

    [tex]\vec D = \vec P_b - \vec P_a[/tex]
    and you need to dot it into a unit vector in that direction.

    No, but it probably has something to do with the first question.
     
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