The connection between the Pivot Vector and quaternion parameterizations of vehicle attitude transformation was investigated to enhance the understanding of each parameter set. Attitude transformations using quaternions involve special product rules for axial rotations in hypercomplex 4-dimensional space. Pivot Vectors involve slewing motion resulting in angular displacements in the 2-dimensional rotation plane. In spite of these differences, Pivot Vectors and quaternions share the same rule for combining rotational transformations and the signature half angle rotation parameter. The Pivot Vector Method defines an attitude transformation by the slewing motion of an axis extending from the center of a unit sphere to its surface. Two Pivot Vectors that also reside in the equatorial plane drive the axis along a portion of a great circle arc in the equatorial plane. A 180 degree rotation about the first Pivot Vector followed by a 180 degree rotation about the second Pivot Vector slews the axis by twice the angular separation between the Pivot Vectors. This explains why the angle between Pivot Vectors is one half the desired rotation angle. The slewing motion of the axis in the equatorial plane produces a rotation about the sphere’s polar axis that applies to all points on the spherical surface, thereby, changing the longitude of each point on the surface while leaving the associated latitude value unchanged. This feature clearly shows that rotations are 2-dimensional. Two sequential transformations are combined by aligning the second Pivot Vector of the first transformation with the first Pivot Vector of the second transformation, even if the Pivot Vector pairs lie in different rotation planes. The linking of the Pivot Vector pairs is achieved because the two 180 degree rotations at the junction cancel, leaving the remaining Pivot Vectors to define the combined transformation. The linking of two Pivot Vector pairs into a single Pivot Vector pair clarifies the geometry of combining rotational transformations and leads to the composition rule for both Pivot Vectors and quaternions. The associated rotational quaternion can be easily derived, since its vector component is the cross product of the Pivot Vectors and its scalar component is the dot product of the Pivot Vectors. A Pivot Vector pair can be obtained from the associated quaternion once its clocking location in the equatorial plane is defined. The quaternion equation to rotate a vector is given a geometric interpretation using the associated Pivot Vectors.