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The bivector a ∧ b has an attitude (or direction) of the plane spanned by a and b, has an area that is a scalar multiple of any reference plane segment with the same attitude (and in geometric algebra, it has a magnitude equal to the area of the parallelogram with edges a and b), and has an orientation being the side of a on which b lies ...
This choice of function results in the following formulation of Maxwell's equations: ′ = ′ ′ = + (′) Several features about Maxwell's equations in the Coulomb gauge are as follows. Firstly, solving for the electric potential is very easy, as the equation is a version of Poisson's equation .
In electromagnetism, the electromagnetic tensor or electromagnetic field tensor (sometimes called the field strength tensor, Faraday tensor or Maxwell bivector) is a mathematical object that describes the electromagnetic field in spacetime.
Examples of geometric algebras applied in physics include the spacetime algebra (and the less common algebra of physical space). Geometric calculus , an extension of GA that incorporates differentiation and integration , can be used to formulate other theories such as complex analysis and differential geometry , e.g. by using the Clifford ...
A well written multiple-choice question avoids obviously wrong or implausible distractors (such as the non-Indian city of Detroit being included in the third example), so that the question makes sense when read with each of the distractors as well as with the correct answer. A more difficult and well-written multiple choice question is as follows:
The simple rotation in the zw-plane by an angle θ has bivector e 34 θ, a simple bivector. The double rotation by α and β in the xy-plane and zw-planes has bivector e 12 α + e 34 β, the sum of two simple bivectors e 12 α and e 34 β which are parallel to the two planes of rotation and have magnitudes equal to the angles of rotation.
A bivector is an oriented plane element, in much the same way that a vector is an oriented line element. Given two vectors a and b, one can view the bivector a ∧ b as the oriented parallelogram spanned by a and b. The cross product is then obtained by taking the Hodge star of the bivector a ∧ b, mapping 2-vectors to vectors:
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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