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Parallel plane segments with the same orientation and area corresponding to the same bivector a ∧ b. [1] In mathematics, a bivector or 2-vector is a quantity in exterior algebra or geometric algebra that extends the idea of scalars and vectors. Considering a scalar as a degree-zero quantity and a vector as a degree-one quantity, a bivector is ...
A two-vector or bivector [1] is a tensor of type () and it is the dual of a two-form, meaning that it is a linear functional which maps two-forms to the real numbers (or more generally, to scalars). The tensor product of a pair of vectors is a two-vector. Then, any two-form can be expressed as a linear combination of tensor products of pairs of ...
The torque or curl is then a normal vector field in this 3rd dimension. By contrast, geometric algebra in 2 dimensions defines these as a pseudoscalar field (a bivector), without requiring a 3rd dimension. Similarly, the scalar triple product is ad hoc, and can instead be expressed uniformly using the exterior product and the geometric product.
On 18 January 2010, ABC News reported Trijicon was placing references to verses in the Bible in the serial numbers of sights sold to the United States Armed Forces. [1] The "book chapter:verse" cites were appended to the model designation, and the majority of the cited verses are associated with light in darkness, referencing Trijicon's specialization in illuminated optics and night sights.
A bivector is an element of the antisymmetric tensor product of a tangent space with itself. In geometric algebra, also, a bivector is a grade 2 element (a 2-vector) resulting from the wedge product of two vectors, and so it is geometrically an oriented area, in the same way a vector is an oriented line segment.
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Mark 8 is the eighth chapter of the Gospel of Mark in the New Testament of the Christian Bible. It contains two miracles of Jesus , Peter's confession that he believes Jesus is the Messiah , and Jesus' first prediction of his own death and resurrection .