$1.$ Let u$=[2$y$^(2),2$z$,3$x$],$v$=[$xy$,$zy$^(2),3$xz$],$f$=2$xz$-3$xy$+4$z$,$g$=2$xyz$^(2).$ Calculate the

following expressions:

$($a$)$ curl $($u$+$v$),$

$($b$)$ div$($uxv$)$

$($c$)$ v $*$ curl u$,$

$($d$)$ u$*$curlv$,$

$($e$)$

$2.$ For the set of vectors A$=3$ai$-2$cj$-5$bk$,$B$=4$i$-2$j$+3$k$,$C$=2$i$+12$j$-3$k$.$

$($a$)$ Calculate B$*($C$\backslash$times A$).$

$($b$)$ Calculate A$\backslash$times $($C$-$B$)$

$($c$)$ What is the angle between A and C $?($Keep variable in cosine function$)$

$($d$)$ What is the projection of A on B$\backslash$times C $?$

$($e$)$ Find the volume of parallelepiped having $($B$-$C$),$A and B as concurrent edges.