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  2. Dot product - Wikipedia

    en.wikipedia.org/wiki/Dot_product

    In mathematics, the dot product or scalar product [note 1] is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors), and returns a single number. In Euclidean geometry , the dot product of the Cartesian coordinates of two vectors is widely used.

  3. Triple product - Wikipedia

    en.wikipedia.org/wiki/Triple_product

    The scalar triple product (also called the mixed product, box product, or triple scalar product) is defined as the dot product of one of the vectors with the cross product of the other two. Geometric interpretation

  4. Geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Geometric_algebra

    Geometrically, and are parallel if their geometric product is equal to their inner product, whereas and are perpendicular if their geometric product is equal to their exterior product. In a geometric algebra for which the square of any nonzero vector is positive, the inner product of two vectors can be identified with the dot product of ...

  5. 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 .

  6. Euclidean plane - Wikipedia

    en.wikipedia.org/wiki/Euclidean_plane

    where · is the dot product and r: [a, b] → C is a bijective parametrization of the curve C such that r(a) and r(b) give the endpoints of C. A double integral refers to an integral within a region D in R 2 of a function f ( x , y ) , {\displaystyle f(x,y),} and is usually written as:

  7. Scalar projection - Wikipedia

    en.wikipedia.org/wiki/Scalar_projection

    where the operator denotes a dot product, ^ is the unit vector in the direction of , ‖ ‖ is the length of , and is the angle between and . [ 1 ] The term scalar component refers sometimes to scalar projection, as, in Cartesian coordinates , the components of a vector are the scalar projections in the directions of the coordinate axes .

  8. 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.

  9. Vector multiplication - Wikipedia

    en.wikipedia.org/wiki/Vector_multiplication

    In mathematics, vector multiplication may refer to one of several operations between two (or more) vectors. It may concern any of the following articles: Dot product – also known as the "scalar product", a binary operation that takes two vectors and returns a scalar quantity. The dot product of two vectors can be defined as the product of the ...