Frame $2$ is initially coincident with Frame $1.$ Then Frame $2$ is rotated about $x_2$ by $60$ deg and then $Z_2$ by $45$ deg. Finally, the origin of $\{2\}$ is translated to $[x_1,Y_1,Z_1{]}^T=[6-5{]}^T.$

$($a$)$ Find the transformation matrix $T_2^1$ in the order given. $(5$ Marks$)$

$($b$)$ A point in Frame $\{2\}$ is $P^2=[2,-1,6{]}^T,$ Find the coordinates of this in Frame $\{1\}.(5-$Marks$)$