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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.
A multiple choice question, with days of the week as potential answers. Multiple choice (MC), [1] objective response or MCQ(for multiple choice question) is a form of an objective assessment in which respondents are asked to select only the correct answer from the choices offered as a list.
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 ...
The test had 75 multiple choice questions that were to be answered in one hour. All questions had five answer choices. Students received 1 point for every correct answer, lost ¼ of a point for each incorrect answer, and received 0 points for questions left blank. This score was then converted to a scaled score of 200–800.
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:
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.