A particle collides with a surface, at velocity vector $\displaystyle v$. The normal vector for the point at which is collides is vector $\displaystyle n$. $\displaystyle \hat v$ and $\displaystyle \hat n$ are the unit vectors for v and a respectively.

1) Using the fact that angle of incident = angle of reflection, what is the new vector $\displaystyle o$, which represents the outgoing velocity, assuming there is no loss of energy.

2) Given a coefficient of restitution, c, how would the vector $\displaystyle o$ differ?