A force F $=(5\mathrm{.}30$N$)$i $+(7\mathrm{.}30$N$)$j $+(3\mathrm{.}20$N$)$k acts on a $1\mathrm{.}40$ kg mobile object that moves from an initial position of d$($sub i$)=(7\mathrm{.}80$m$)$i $+(5\mathrm{.}20$m$)$j $+(7\mathrm{.}90$m$)$k to a final position of d$($sub f$)=(3\mathrm{.}30$m$)$i $+(4\mathrm{.}30$m$)$j $+(4\mathrm{.}90$m$)$k in $3\mathrm{.}60$s$.$ Find $($a$)$ the work done on the object by the force in the $3\mathrm{.}60$s interval, $($b$)$ the average power due to the force during that interval, and $($c$)$ the angle between vectors d $($sub i$)$ and d $($sub f$).$