In VECTRIX NOTATION Consider the $3$D spherical pendulum of length $l$ shown in Figure $2.$ The frame $F_a$ is fixed to the ground and frame $F_b$ is fixed to the pendulum, with $b^3$ pointing in the direction of the pendulum rod. An intermediate frame $F_l$ exists, but is not shown in the diagram. The relationship between the frames is

$F_a{C}_3(phi)F_l{C}_2(theta)F_b$

$($a$)$ Find $$ ra resolved in $F_b.$

$($b$)$ Find $a\frac{w}{a}\frac{?}{a}=v\frac{w}{a^{*a}}$ resolved in $F_b.$

Figure $2$: A $3$D spherical pendulum.