Vectors vec$(A)$ and vec$(B)$ lie in an xy plane. vec$(A)$ has magnitude $5\mathrm{.}2$ and angle $107$;vec$(B)$ has components $B_x=-3\mathrm{.}20$ and $B_y=-5\mathrm{.}76.($a$)$ What is $5$vec$(A)*vec(B)?$ What is $4$vec$(A)3$vec$(B)$ in unit$-$vector notation $(($b$),($c$)$ and $($d$)$ for hat$(i),$hat$(j)$ and hat$(k)$ components respectively$)?($e$)$ What is the angle between the directions of vec$(A)$ and $4$vec$(A)3$vec$(B)?$ What is vec$(A)+3\mathrm{.}00$hat$(k)$ in unit$-$vector notation $((f),($g$)$ and $($h$)$ for hat$(i),$hat$(j)$ and hat$(k)$ components respectively$)$ and magnitude$-$angle notation with spherical coordinates $((i)$ for magnitude, $($j$)$ for $$ and $(k)$ for $)?$