ABSTRACT
Multiplication in the point model is associative and distributes through addition, but as usual multiplication is not commutative since As in the plane model, two important subalgebras reside inside the point model of Clifford algebra: the quaternions and the dual quaternions. These definitions describe the geometry associated with the basis multivectors of the point model of the Clifford algebra for the dual quaternions. Although these definitions seem quite natural, the authors need to understand how these definitions relate back to the geometry associated with the dual quaternions. They will explore these connections and extend these definitions to representations for arbitrary vectors, points, lines, and planes in 3-dimensions. They show that multiplication by maps vectors, points, and planes in the space of dual quaternions into the corresponding vectors, points, and planes in the point model of Clifford algebra.
