structural:expansion, structural:summarization, information:extraction, linguistic:translation, linguistic:paraphrasing
Properties and operations

The following section uses the Cartesian coordinate system with basis vectors e 1 = (1, 0, 0), e 2 = (0, 1, 0), e 3 = (0, 0, 1) {\displaystyle {\mathbf {e} }_{1}=(1,0,0),\ {\mathbf {e} }_{2}=(0,1,0),\ {\mathbf {e} }_{3}=(0,0,1)} and assumes that all vectors have the origin as a common base point. A vector a will be written as a = a 1 e 1 + a 2 e 2 + a 3 e 3. {\displaystyle {\mathbf {a} }=a_{1}{\mathbf {e} }_{1}+a_{2}{\mathbf {e} }_{2}+a_{3}{\mathbf {e} }_{3}.}