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  2. Euclidean vector - Wikipedia

    en.wikipedia.org/wiki/Euclidean_vector

    A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space.

  3. 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.

  4. Parallelogram law - Wikipedia

    en.wikipedia.org/wiki/Parallelogram_law

    Vectors involved in the parallelogram law. In a normed space, the statement of the parallelogram law is an equation relating norms: ‖ ‖ + ‖ ‖ = ‖ + ‖ + ‖ ‖,.. The parallelogram law is equivalent to the seemingly weaker statement: ‖ ‖ + ‖ ‖ ‖ + ‖ + ‖ ‖, because the reverse inequality can be obtained from it by substituting (+) for , and () for , and then simplifying.

  5. Vector (mathematics and physics) - Wikipedia

    en.wikipedia.org/wiki/Vector_(mathematics_and...

    Vector addition and scalar multiplication: a vector v (blue) is added to another vector w (red, upper illustration). Below, w is stretched by a factor of 2, yielding the sum v + 2w . In mathematics and physics , a vector space (also called a linear space) is a set whose elements, often called vectors , can be added together and multiplied ...

  6. Vector notation - Wikipedia

    en.wikipedia.org/wiki/Vector_notation

    Using the algebraic properties of subtraction and division, along with scalar multiplication, it is also possible to “subtract” two vectors and “divide” a vector by a scalar. Vector subtraction is performed by adding the scalar multiple of −1 with the second vector operand to the first vector operand. This can be represented by the ...

  7. Vector algebra - Wikipedia

    en.wikipedia.org/wiki/Vector_algebra

    In mathematics, vector algebra may mean: The operations of vector addition and scalar multiplication of a vector space; The algebraic operations in vector calculus (vector analysis) – including the dot and cross products of 3-dimensional Euclidean space; Algebra over a field – a vector space equipped with a bilinear product

  8. Comparison of vector algebra and geometric algebra - Wikipedia

    en.wikipedia.org/wiki/Comparison_of_vector...

    Since the vector term of the vector bivector product the name dot product is zero when the vector is perpendicular to the plane (bivector), and this vector, bivector "dot product" selects only the components that are in the plane, so in analogy to the vector-vector dot product this name itself is justified by more than the fact this is the non ...

  9. Classical Hamiltonian quaternions - Wikipedia

    en.wikipedia.org/wiki/Classical_Hamiltonian...

    Hamilton defined addition of vectors in geometric terms, by placing the origin of the second vector at the end of the first. [9] He went on to define vector subtraction. By adding a vector to itself multiple times, he defined multiplication of a vector by an integer , then extended this to division by an integer, and multiplication (and ...