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  2. Cross product - Wikipedia

    en.wikipedia.org/wiki/Cross_product

    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 .

  3. Lists of vector identities - Wikipedia

    en.wikipedia.org/wiki/Lists_of_vector_identities

    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.

  4. Vector algebra relations - Wikipedia

    en.wikipedia.org/wiki/Vector_algebra_relations

    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.

  5. Right-hand rule - Wikipedia

    en.wikipedia.org/wiki/Right-hand_rule

    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.

  6. Distance from a point to a line - Wikipedia

    en.wikipedia.org/wiki/Distance_from_a_point_to_a...

    where is the cross product of the vectors and and where ‖ ‖ is the vector norm of . A P → = P − A {\displaystyle {\overrightarrow {\mathrm {AP} }}=P-A} Note that cross products only exist in dimensions 3 and 7 and trivially in dimensions 0 and 1 (where the cross product is constant 0).

  7. Triple product - Wikipedia

    en.wikipedia.org/wiki/Triple_product

    This also relates to the handedness of the cross product; the cross product transforms as a pseudovector under parity transformations and so is properly described as a pseudovector. The dot product of two vectors is a scalar but the dot product of a pseudovector and a vector is a pseudoscalar, so the scalar triple product (of vectors) must be ...

  8. Künneth theorem - Wikipedia

    en.wikipedia.org/wiki/Künneth_theorem

    The map from the sum to the homology group of the product is called the cross product. More precisely, there is a cross product operation by which an i -cycle on X and a j -cycle on Y can be combined to create an ( i + j ) {\displaystyle (i+j)} -cycle on X × Y {\displaystyle X\times Y} ; so that there is an explicit linear mapping defined from ...

  9. Dyadics - Wikipedia

    en.wikipedia.org/wiki/Dyadics

    The dot product takes in two vectors and returns a scalar, while the cross product [a] returns a pseudovector. Both of these have various significant geometric interpretations and are widely used in mathematics, physics, and engineering. The dyadic product takes in two vectors and returns a second order tensor called a dyadic in this context. A ...