The Clifford algebra for the group of rigid body motions is described. Linear elements, that is points, lines and planes are identified as homogeneous elements in the algebra. In each case the action of the group of rigid motions on the linear elements is found. The relationships between these linear elements are found in terms of operations in the algebra. That is, incidence relations, the conditions for a point to lie on a line for example are found. Distance relations, like the distance between a point and a plane are found. Also the meet and join of linear elements, for example, the line determined by two planes and the plane defined by a line and a point, are found. Finally three examples of the use of the algebra are given: a computer graphics problem on the visibility of the apparent crossing of a pair of lines, an assembly problem concerning a double peg-in-hole assembly, and a problem from computer vision on finding epipolar lines in a stereo vision system.

A novel three-dimensional model of tertiary interactions in the core region of the eukaryotic selenocysteine tRNA is proposed based on the analysis of available nucleotide sequences. The model features the 7/5 tRNASec secondary structure characterized by seven and five base pairs in the acceptor and T-stems, respectively, and four nucleotides in the connector region between the acceptor and D-stems. The model suggests a unique system of tertiary interactions in the area between the major groove of the D-stem and the first base pair of the extra arm that provides a rigid orientation of the extra arm and contributes to the overall stability of the molecule. The model is consistent with available experimental data on serylation, selenylation, and phosphorylation of different tRNASec mutants. The important similarity between the proposed model and the structure of the tRNASer is shown. Based on this similarity, the ability of some tRNASer mutants to be serylated, selenylated, and phosphorylated was evaluated and found to be in a good agreement with experimental data.