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A bound vector is defined as the combination of an ordinary vector quantity and a point of application or point of action. [ 1 ] [ 4 ] Bound vector quantities are formulated as a directed line segment , with a definite initial point besides the magnitude and direction of the main vector.
A vector quantity is a vector-valued physical quantity, including units of measurement and possibly a support, formulated as a directed line segment. A vector is frequently depicted graphically as an arrow connecting an initial point A with a terminal point B, [3] and denoted by .
In the theory of vector measures, Lyapunov's theorem states that the range of a finite-dimensional vector measure is closed and convex. [1] [2] [3] In fact, the range of a non-atomic vector measure is a zonoid (the closed and convex set that is the limit of a convergent sequence of zonotopes). [2]
A vector-valued function, also referred to as a vector function, is a mathematical function of one or more variables whose range is a set of multidimensional vectors or infinite-dimensional vectors. The input of a vector-valued function could be a scalar or a vector (that is, the dimension of the domain could be 1 or greater than 1); the ...
In science and engineering, the weight of an object is a quantity associated with the gravitational force exerted on the object by other objects in its environment, although there is some variation and debate as to the exact definition. [1] [2] [3] Some standard textbooks [4] define weight as a vector quantity, the gravitational force acting on ...
Assuming that the temperature T is an intensive quantity, i.e., a single-valued, continuous and differentiable function of three-dimensional space (often called a scalar field), i.e., that = (,,) where x, y and z are the coordinates of the location of interest, then the temperature gradient is the vector quantity defined as
In classical electromagnetism, magnetic vector potential (often called A) is the vector quantity defined so that its curl is equal to the magnetic field: =. Together with the electric potential φ , the magnetic vector potential can be used to specify the electric field E as well.
The kinetic energy is a scalar and the momentum is a vector, and these two quantities must be represented by a scalar and a vector operator, respectively. By the latter in particular, we mean an operator whose expected values in the initial and the rotated states are p z ^ {\displaystyle p{\mathbf {\hat {z}} }} and p x ^ {\displaystyle p ...