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Given a point P(1, 3, 2) in a reference coordinate system (O‐XYZ), determine its new position P′ after the following operations: (i) rotate 45° with respect to the X axis, (ii) translate it with a vector of (0.5, 2, 1), (iii) rotate −30° with respect to the Z axis, and (iv) mirror the position about the XY plane.