Two vectors are given by vec$(a)=(4\mathrm{.}0m)hat(i)-(3\mathrm{.}0m)hat(j)+(1\mathrm{.}0m)hat(k)$ and vec$(b)=(-1\mathrm{.}0m)hat(i)+(1\mathrm{.}0m)hat(j)+(4\mathrm{.}0m)hat(k)*ln$ unit$-$vector notation, find $($a$)$ vec$(a)+$vec$(b),($b$)$ vec$(a)-$vec$(b),$ and $($c$)$ a third vector vec$(c)$ such that vec$(a)-$vec$(b)+$vec$(c)=0$