Forces Vectors And Dot Products

[ewan_71]

Hello all ,

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 !

Ewan.

 

[LCKurtz]

Hello all ,

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

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

$$\vec P_a = \langle p_1,p_2,p_3\rangle,\ \vec P_b = \langle q_1,q_2,q_3\rangle$$

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

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

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

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