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What are the coordinates of a point on a rigid body after a rotation in 3D Euclidean space, given the initial coordinates and a center of rotation

Main question Let ($x_p$, $y_p$, $z_p$) be the initial coordinates of a point $P$ on a rigid body in a right-handed 3D Euclidean space. Let ($x_r$, $y_r$, $z_r$) be the coordinates of a center of ...
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Projection of the area of a bounded plane over other bounded plane

I have two bounded planes $\pi$ and $\rho$ in three dimensional space. Each plane is bounded by a coplanar rectangle. How can I find the orthogonal projection area of $\pi$ over $\rho$? Thanks in ...