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In mathematics and physics, the right-hand rule is a convention and a mnemonic, utilized to define the orientation of axes in three-dimensional space and to determine the direction of the cross product of two vectors, as well as to establish the direction of the force on a current-carrying conductor in a magnetic field.
The cross product with respect to a right-handed coordinate system. In mathematics, the cross product or vector product (occasionally directed area product, to emphasize its geometric significance) is a binary operation on two vectors in a three-dimensional oriented Euclidean vector space (named here ), and is denoted by the symbol .
Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.
In mathematics and computer programming, the order of operations is a collection of rules that reflect conventions about which operations to perform first in order to evaluate a given mathematical expression. These rules are formalized with a ranking of the operations.
As it does not change at all, the Levi-Civita symbol is, by definition, a pseudotensor. As the Levi-Civita symbol is a pseudotensor, the result of taking a cross product is a pseudovector, not a vector. [5] Under a general coordinate change, the components of the permutation tensor are multiplied by the Jacobian of the transformation matrix ...
The following are important identities in vector algebra.Identities that only involve the magnitude of a vector ‖ ‖ and the dot product (scalar product) of two vectors A·B, apply to vectors in any dimension, while identities that use the cross product (vector product) A×B only apply in three dimensions, since the cross product is only defined there.
The rule of three [1] was a historical shorthand version for a particular form of cross-multiplication that could be taught to students by rote. It was considered the height of Colonial maths education [ 2 ] and still figures in the French national curriculum for secondary education, [ 3 ] and in the primary education curriculum of Spain.
In mathematics, the symbol × has a number of uses, including Multiplication of two numbers, where it is read as "times" or "multiplied by" [1] Cross product of two vectors, where it is usually read as "cross" Cartesian product of two sets, where it is usually read as "cross" [7]