A $12$ N force with a fixed orientation does work on a particle as the particle moves through displacement vec d $=(4$ hat i $-4$ hat j $+4$ hat k $)$ m$.$ What is the angle between the force and the displacement if the change in the particle's kinetic energy is $($a$)+8\mathrm{.}31$ J and $($b$)-8\mathrm{.}31$ J$?.$