Let $F(t)=cos(2t)i+4tj+t^{3}k$ and $G(t)=t^{3}cos(2t)i+t^{3}j+2e^{3t}k,$ find $F(t)*G(t).$

$A.t^{3}co{s}^2(2t)i+4t^{4}j+2t^3{e}^{3t}k$

$B.8t{e}^{3t}-t^6+(t^6-2e^{3t})cos(2t)+(t^3-4t^4)cos(2t)$

$C.t^{3}co{s}^2(2t)+4t^4+2t^3{e}^{3t}$

$D.(t^{3}co{s}^2(2t)+4t^4+2t^3{e}^{3t})j$

$E.(8t{e}^{3t}-t^6)i+(t^6-2e^{3t})cos(2t)j+(t^3-4t^4)cos(2t)k$