A force F $=(8\mathrm{.}60$ N$)$i $+(3\mathrm{.}30$ N$)$j $+(2\mathrm{.}50$N$)$k acts on a $8\mathrm{.}80$ kg mobile object that moves from an initial position of d$=(2\mathrm{.}90$m$)$i $+(4\mathrm{.}00$m$)$j $+(3\mathrm{.}50$m$)$k to a final position of d$=(3\mathrm{.}20$m$)$i $+(6\mathrm{.}00$m$)$j $+(8\mathrm{.}60$m$)$k in $8\mathrm{.}90$s$.$ Find $($a$)$ the work done on the object by the force in the $8\mathrm{.}90$s interval, $($b$)$ the average power due to the force during the interval, and $($c$)$ the angle between vectors di and df$.$