$(30$ points$)$ Consider that a rigid body with unit vectors hat$(b)$ move with respect to

the inertial frame hat$(e).$ At the initial time, hat$(e{)}_1=$hat$(b{)}_1,$hat$(e{)}_2=$hat$(b{)}_2$ and hat$(e{)}_3=$hat$(b{)}_3.$ The final

orientation of hat$(b)$ with respect to hat$(e)$ is given by:

$\frac{?}{\text{b}\text{a}\text{r}}(u)=-3$hat$(e{)}_1-2$hat$(e{)}_2+$hat$(e{)}_3$

$=-45o_{?}$

The final DCM from $e$ to $b$ is: