bivector sentence in Hindi
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- In 3D, rotations have three degrees of freedom, a degree for each linearly independent plane ( bivector ) the rotation can take place in.
- Loosely speaking the length of a vector is a length, length of a bivector is area, and the length of a trivector is volume.
- In general ( and not necessarily for Euclidean vectors ) the rotation of a vector space equipped with a quadratic form can be expressed as a bivector.
- The exterior product of two vectors is antisymmetric, so is the negation of the bivector, producing the opposite orientation, and is the zero bivector.
- The exterior product of two vectors is antisymmetric, so is the negation of the bivector, producing the opposite orientation, and is the zero bivector.
- A bivector has a real square if and only if it is simple, and only simple bivectors can be represented geometrically by an oriented plane area.
- This is only true in two dimensions, so properties of the bivector in two dimensions that depend on commutativity do not usually generalise to higher dimensions.
- The bivector " F " " ab " yields a skew-symmetric linear operator defined by lowering one index with the metric.
- Under the geometric product, bivectors have negative square : the bivector \ scriptstyle \ hat x \ hat y describes the \ scriptstyle xy-plane.
- The derivatives that appear in Maxwell's equations are vectors and electromagnetic fields are represented by the Faraday bivector "'F " '.
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