Vector (mathematics and physics)In mathematics and physics, a vector is a generalization of a single number. It may denote a vector quantity, i.e., physical quantity that cannot be expressed by a single scalar quantity. The term may also be used to refer to elements of vector spaces, that can be added together and multiplied ("scaled") by scalars. In some contexts, vectors are tuples, which are finite sequences (of numbers or other objects) of a fixed length.Euclidean vectorIn mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space. A vector quantity is a vector-valued physical quantity, including units of measurement and possibly a support, formulated as a directed line segment.
Direction (geometry)In geometry, direction, also known as spatial direction, vector direction or relative direction, is the common characteristic of all rays which coincide when translated to share a common endpoint; equivalently, it is the common characteristic of vectors (such as the relative position between a pair of points) which can be made equal by scaling (by some positive scalar multiplier). Two vectors sharing the same direction are said to be codirectional or equidirectional.
Physical quantityA physical quantity (or simply quantity) is a property of a material or system that can be quantified by measurement. A physical quantity can be expressed as a value, which is a pair of a numerical value and a unit of measurement. For example, the physical quantity mass, symbol m, can be quantified as m=n kg, where n is the numerical value and kg is the unit symbol (for kilogram). Vector quantities have, besides numerical value and unit, direction or orientation in space.
Unit of measurementA unit of measurement, or unit of measure, is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity. Any other quantity of that kind can be expressed as a multiple of the unit of measurement, For example, a length is a physical quantity. The metre (symbol: m) is a unit of length that represents a definite predetermined length.
Three-dimensional spaceGeometric model of the physical spaceA representation of a three-dimensional Cartesian coordinate systemIn geometry, a three-dimensional (3D) space is a mathematical space in which three values (termed coordinates) are required to determine the position of a point. Alternatively, it can be referred to as 3-space or, rarely, tri-dimensional space.
Dimensionless quantityDimensionless quantities, or quantities of dimension one, are quantities with no associated units of measurement. These may be ratios of quantities with the same physical units or ratios of dimensionally equal products with identical units. For instance, alcohol by volume (ABV) represents a volumetric ratio; its value remains independent of the specific units of volume used, such as in milliliters per milliliter (mL/mL).
Position (geometry)In geometry, a position or position vector, also known as location vector or radius vector, is a Euclidean vector that represents a pointP in space. Its length represents the distance in relation to an arbitrary reference originO, and its direction represents the angular orientation with respect to given reference axes.
SpaceSpace is a three-dimensional continuum containing positions and directions. In classical physics, physical space is often conceived in three lineardimensions. Modern physicists usually consider it, with time, to be part of a boundless four-dimensionalcontinuum known as spacetime. The concept of space is considered to be of fundamental importance to an understanding of the physical universe.
Norm (mathematics)Length in a vector spaceIn mathematics, a norm is a function from a real or complex vector space to the non-negative real numbers that behaves in certain ways like the distance from the origin: it commutes with scaling, obeys a form of the triangle inequality, and is zero only at the origin.
Natural scienceNatural science or empirical science is a branch of science concerned with the description, understanding, and prediction of natural phenomena, based on empirical evidence from observation and experimentation. Mechanisms such as peer review and reproducibility of findings are used to try to ensure the validity of scientific advances. Natural science can be divided into two main branches: life science and physical science. Life science is alternatively known as biology.
Value (mathematics)In mathematics, a mathematical value is a broad term that refers to any definite entity that can be manipulated with operators according to the well-defined rules of its mathematical system. Certain values can correspond to the real world, although most values in mathematics generally exist purely as abstract objects with no connection to the real world. Numerical valuesNumbers (specifically the reals) are values that represent quantities.*As an Amazon Associate I earn from qualifying purchases.