P$3.$ Given the excess hyperbolic velocity vector, v$\_(\backslash$infty $0),$ at the entrance and exit of the SOI of Mars, find

the minimum flyby altitude z$\_($p$),$ the inclination and the eccentricity of the flyby trajectory.

Entrt of SOI: v$\_($c$)=[-9\mathrm{.}65310,-12\mathrm{.}55056,-4\mathrm{.}64086]$k$($m$)/($s$)$

Exit of SOI: v$\_(\backslash$alpha $)=[-8\mathrm{.}52640,-13\mathrm{.}06368,-5\mathrm{.}36977]$k$($m$)/($s$)$