Vector norm in the context of "Radial velocity"

In the natural sciences, a vector quantity (also known as a vector physical quantity, physical vector, or simply vector) is a vector-valued physical quantity.It is typically formulated as the product of a unit of measurement and a vector numerical value (unitless), often a Euclidean vector with magnitude and direction.For example, a position vector in physical space may be expressed as three Cartesian coordinates with SI unit of meters.

In physics and engineering, particularly in mechanics, a physical vector may be endowed with additional structure compared to a geometrical vector.A bound vector is defined as the combination of an ordinary vector quantity and a point of application or point of action. Bound vector quantities are formulated as a directed line segment, with a definite initial point besides the magnitude and direction of the main vector.For example, a force on the Euclidean plane has two Cartesian components in SI unit of newtons (describing the magnitude and direction of the force) and an accompanying two-dimensional position vector in meters (describing the point of application of the force), for a total of four numbers on the plane (and six in space).A simpler example of a bound vector is the translation vector from an initial point to an end point; in this case, the bound vector is an ordered pair of points in the same position space, with all coordinates having the same quantity dimension and unit (length and meters).A sliding vector is the combination of an ordinary vector quantity and a line of application or line of action, over which the vector quantity can be translated (without rotations).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.

A spatial gradient is a gradient whose components are spatial derivatives, i.e., rate of change of a given scalar physical quantity with respect to the position coordinates in physical space. Homogeneous regions have spatial gradient vector norm equal to zero.When evaluated over vertical position (altitude or depth), it is called vertical derivative or vertical gradient; the remainder is called horizontal gradient component, the vector projection of the full gradient onto the horizontal plane.

The relative velocity of an object B with respect to an observer A, denoted ${\displaystyle \mathbf {v} _{B\mid A}}$ (also ${\displaystyle \mathbf {v} _{BA}}$ or ${\displaystyle \mathbf {v} _{B\operatorname {rel} A}}$), is the velocity vector of B measured in the rest frame of A.The relative speed is the vector norm of the relative velocity, ${\displaystyle v_{B\mid A}=\|\mathbf {v} _{B\mid A}\|}$.

In mathematics, particularly in calculus, a stationary point of a differentiable function of one variable is a point on the graph of the function where the function's derivative is zero. Informally, it is a point where the function "stops" increasing or decreasing (hence the name).

For a differentiable function of several real variables, a stationary point is a point on the surface of the graph where all its partial derivatives are zero (equivalently, the gradient has zero norm).The notion of stationary points of a real-valued function is generalized as critical points for complex-valued functions.