Non$-$cartesian vector fields $!$Problem $5\mathrm{.}1$ Line integrals $($i$)$ F $=$ x$2$y $$x $+$ xz $$y $2$yz $$z and $$ is the curve whose parametric equation is r$($s$)=$x $4$s $+$y $2$s$2+$z s$3.$ Evaluate the line integral $!$ r$2$ r$1$ F $$ dr along the path r$($s$)$ which joins the points r$1=(0,0,0)$ and r$2=(4,2,1).[3]($ii$)$ In spherical polar coordinates $($r$,$ $,),$ F $=$r r$2+$ $$ re$2$ $+$ r$3$ cos $.$ Calculate $$ F $.[3]($iii$)$ In spherical polar coordinates $($r$,$ $,),$ F $=$r r$2+$ $$ r e$2$ $+$ r$3$ cos $,$ Calculate $$ F$.$