 This replacement is useful, because now it is only the rotation matrix formula_102 that is changing in time and not the reference vector formula_103, as the rigid body rotates about point .Also, since the three columns of the rotation matrix represent the three versors of a reference frame rotating together with the rigid body, any rotation about any axis becomes now visible, while the vector formula_99 would not rotate if the rotation axis were parallel to it, and hence it would only describe a rotation about an axis perpendicular to it (i.e., it would not see the component of the angular velocity pseudovector parallel to it, and would only allow the computation of the component perpendicular to it).The position of the particle is now written as