As an assignment for uni I need to figure out an algorithm that explodes a particle of mass $m$, velocity $v$, into $n$ pieces.
For the first part of the assignment, the particle has mass $m$, velocity of $0$, the particle explodes into 6 equal pieces, and is not affected by gravity.
The problem I'm having is, how do I determine 6 equidistant unit vectors in three dimensions?
Assuming I need an initial vector, a unit vector in the direction of $v$ (the initial particle velocity) will do. In the initial case, where $v$ is $(+0, +0, +0)$, let the initial unit vector be in an arbitrary direction.
Also, how do I determine what speed each sub-particle will have? I know that the sum of sub-particle momentum will be equal to the momentum of the initial particle, and because each particle has the same mass they will each have the same speed... Do I need an explosion Force amount or something?