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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. Distance from a point to a line - Wikipedia

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

    Also, let Q = (x 1, y 1) be any point on this line and n the vector (a, b) starting at point Q. The vector n is perpendicular to the line, and the distance d from point P to the line is equal to the length of the orthogonal projection of on n. The length of this projection is given by:

  4. Norm (mathematics) - Wikipedia

    en.wikipedia.org/wiki/Norm_(mathematics)

    On the -dimensional Euclidean space, the intuitive notion of length of the vector = (,, …,) is captured by the formula [11] ‖ ‖:= + +. This is the Euclidean norm , which gives the ordinary distance from the origin to the point X —a consequence of the Pythagorean theorem .

  5. Dot product - Wikipedia

    en.wikipedia.org/wiki/Dot_product

    The length of a vector is defined as the square root of the dot product of the vector by itself, and the cosine of the (non oriented) angle between two vectors of length one is defined as their dot product. So the equivalence of the two definitions of the dot product is a part of the equivalence of the classical and the modern formulations of ...

  6. Vector notation - Wikipedia

    en.wikipedia.org/wiki/Vector_notation

    In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .

  7. Vector (mathematics and physics) - Wikipedia

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

    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.

  8. Euclidean distance - Wikipedia

    en.wikipedia.org/wiki/Euclidean_distance

    By Dvoretzky's theorem, every finite-dimensional normed vector space has a high-dimensional subspace on which the norm is approximately Euclidean; the Euclidean norm is the only norm with this property. [24] It can be extended to infinite-dimensional vector spaces as the L 2 norm or L 2 distance. [25]

  9. Unit vector - Wikipedia

    en.wikipedia.org/wiki/Unit_vector

    In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e.,