# Mathematics Solution of Vector

Euclidean vector, a geometric entity endowed with magnitude and direction as well as a positive-definite inner product; an element of a Euclidean vector space. In physics, euclidean vectors are used to represent physical quantities that have both magnitude and direction, such as force, in contrast to scalar quantities, which have no direction.

## Mathematics Solution of Vector

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Vectors:

Euclidean vector, a geometric entity endowed with magnitude and direction as well as a positive-definite inner product; an element of a Euclidean vector space. In physics, euclidean vectors are used to represent physical quantities that have both magnitude and direction, such as force, in contrast to scalar quantities, which have no direction.

Vector product, or cross product, an operation on two vectors in a three-dimensional Euclidean space, producing a third three-dimensional Euclidean vector

Burgers vector, a vector that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice

Laplace–Runge–Lenz vector, a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another

Normal vector, or surface normal, a vector that is perpendicular to a (hyper) surface at a point

An element of a vector space

Basis vector, one of a set of vectors (a “basis”) that, in linear combination, can represent every vector in a given vector space

Coordinate vector, in linear algebra, an explicit representation of an element of any abstract vector space

Row vector or column vector, a one-dimensional matrix often representing the solution of a system of linear equations

An element of the real coordinate space Rn

Random vector or multivariate random variable, in statistics, a set of real-valued random variables that may be correlated

Vector projection, also known as the vector resolute or vector component, a linear mapping producing a vector parallel to a second vector

The vector part of a quaternion, a mathematical entity which is one possible generalisation of a vector

Null vector, a vector whose magnitude is zero

Position vector, a vector representing the position of a point in an affine space in relation to a reference point

Displacement vector, a vector that specifies the change in position of a point relative to a previous position

Gradient vector, the vector giving the magnitude and direction of maximum increase of a scalar field

Poynting vector, in physics, a vector representing the energy flux density of an electromagnetic field

Wave vector, a vector representation of the local phase evolution of a wave

Tangent vector, an element of the tangent space of a curve, a surface or, more generally, a differential manifold at a given point.

Gyrovector, a hyperbolic geometry version of a vector

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