Vector Transformation Under an Euler Angle Passive Rotation

Question

Let there be some object in $\mathbb{R}^3$ centered at point $P$ with coordinates $(x_P,y_P,z_P)$. Its orientation is defined by Euler angles $\alpha, \beta, \gamma$ with respect to some reference configuration. We wish to transform to some new, rotated frame (i.e. a passive transformation). The rotation from the initial frame to the new one is defined by the Euler angles $A,B,\Gamma$. What are the new coordinates of the center of the object $Q$ and what are the new Euler angles?