$(10$ 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$(b{)}_2,$hat$(e{)}_2=$hat$(b{)}_3$ and hat$(e{)}_3=$hat$(b{)}_1.$ Note

that e and b are NOT initially aligned $o..$ The final orientation hat$(f)$ of the body

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

$\frac{?}{\text{b}\text{a}\text{r}}(u)=-$hat$(e{)}_1-4$hat$(e{)}_2-2$hat$(e{)}_3$

$=-60$

What is the value of $C_{12}$ for the rotation from $b$ to $f?$

$($a$)0\mathrm{.}5952$

$($b$)-0\mathrm{.}7083$

$($c$)-0\mathrm{.}5952$

$($d$)0\mathrm{.}7083$