In C$++$

Make $8$ Argon particles whose centers are at the corners of a cube of edge length $2.$ The coordinates of the particles are: particle $1$ at $(0,0,0),$ particle $2$ at $(2,0,0),$ particle $3$ at $(0,2,0),$ particle $4$ at $(2,2,0),$ particle $5$ at $(0,0,2),$ particle $6$ at $(2,0,2),$ particle $7$ at $(0,2,2),$ and particle $8$ at $(2,2,2).$ Figure $1$ is shown to help with the visualization of the setup $($particle $1$ at the origin is colored blue$).$ Use Ovito to visualize your system.

$($a$)$ Modify the code to compute the total initial force on each particle exerted by all the other particles. Make sure the code prints out the vector force on each particle, explicitly showing the force's $x,y,z$ components.

$($b$)$ What is the total initial force vector vec$(f)($in reduced units$)$ exerted by all other particles on particle $1?$

$2$

FIG. $1.$ Visualization for problems B$1$ and B$2.$

$($c$)$ Is this force directed toward pushing particle $1$ inside the cube or outside the cube?

Identify the particle $($by its number$)$ that attracts particle $1$ with the least amount of force?