The sketch shows an electric fan that may rotate about three axes. In this sketch XYZ constitute a set of fixed axes, and xyz are attached to the fan blades. The rotations are defined as follows. When the rotation angle β about the fixed vertical Z axis is zero, the pin’s axis aligns with the fixed horizontal Y axis. When the rotation angle γ about the pin is zero, the shaft about which the fan blades spin is horizontal. When the spin angle δ is zero, the x axis is aligned with the axis of the pin. Consider a sequence of rotations in which γ occurs first, followed by β, then δ. Describe the transformation matrix [R] for which   as a set of simple rotation transformations about specific axes. Then identify an alternative sequence in which the rotations β, γ, δ may be executed and still arrive at the same final orientation of xyz relative to XYZ.