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A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
The vector projection (also known as the vector component or vector resolution) of a vector a on (or onto) a nonzero vector b is the orthogonal projection of a onto a straight line parallel to b.
The choice has been controversial: Pfeifer et al. [10] summarize and to a certain extent resolve the century-long dispute between proponents of the Abraham and Minkowski forms (see Abraham–Minkowski controversy). The Poynting vector represents the particular case of an energy flux vector for electromagnetic energy.
When only the magnitude and direction of the vector matter, and the particular initial or terminal points are of no importance, the vector is called a free vector. The distinction between bound and free vectors is especially relevant in mechanics, where a force applied to a body has a point of contact (see resultant force and couple ).
A linear subspace or vector subspace W of a vector space V is a non-empty subset of V that is closed under vector addition and scalar multiplication; that is, the sum of two elements of W and the product of an element of W by a scalar belong to W. [10] This implies that every linear combination of elements of W belongs to W. A linear subspace ...
A graph of the vector-valued function r(z) = 2 cos z, 4 sin z, z indicating a range of solutions and the vector when evaluated near z = 19.5. A common example of a vector-valued function is one that depends on a single real parameter t, often representing time, producing a vector v(t) as the result.
A gay Georgia couple convicted of sickening sexually abuse of their two adopted sons will spend the rest of the lives behind bars.. William and Zachary Zulock, 34 and 36, were each sentenced last ...
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.