Q$3)$

Two frames, $B($black$)$ and $R($red$),$ are initially coincident. One of the frames $R$ is transforming with a series of transformations. These are: rotation about $x-$axis by $,$ rotation about $y-$axis by $,$ rotation about $z-$axis by $,$ translation along $x-$axis by $d_x,$ translation along $y-$axis by $d_y,$ translation along $z$ axis by $d_z,$ respectively. There is a position vector $P_R$ in frame $R$ with coordinates $P_{{?}_{?}}(R)(x_R,y_R,z_R).$ Determine the vector $P_{{?}_{?}}(B)(x_B,y_B,z_B)$ in the frame $B($black$).$

$\backslash$table$[[,,,d_x,d_y,d_z,x_R,y_R,z_R$