A frame $\{B\}$ is initially coincident with frame $\{A\}.\{B\}$ is first rotated about the

$x_B$ axis $($axis of frame $\{B\})$ by angle $$ and then the resulting frame is rotated by $Y_B$ axis

by angle $.$

$($a$)$ Find the rotation matrix $R_B^A($orientation of frame $B$ with respect to $A).$

$($b$)$ Compute $R_B^A$ for $=45$ and $=60.$

$($c$)$ If a vector in frame $\{B\}$ is given by vec$(P{)}^B=\left[\begin{array}{c}5\\ 1\\ 3\end{array}\right],$ what is that vector is frame $\{A\}vec(P{)}^A?$

Plot both the $3$D vectors vec$(P{)}^B$ and vec$(P{)}^A.$