$(a)$ Given a vector field $F(x,y,z)=$xyzi$+(x+2y)j-3x{z}^{2}k.$ Determine the Curl $F$ and Divergence $Fat$ the point $(1,1,2).$

$(b)$ A particle travels along the curve $C$ which $is$ formed $by$ the curve $y=x^2$ from $x=0tox=2$ and the line segment from $(2,4)to(3,4).$ Calculate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F.dr$ given that the force, $F(x,y)=3$xyi$+yj.$

$(c)By$ using Green's Theorem, evaluate ${\displaystyle \underset{C}{\overset{\phantom{}}{}}}F.dr$ along $C$ that $is$ the positively oriented boundary $of$ the region bounded $by$ the triangle formed $by$ the lines $y=0,x=1$ and $y=x$ where $F(x,y)=(2x+y)i+(x{y}^2)j$