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A vector may also result from the evaluation, at a particular instant, of a continuous vector-valued function (e.g., the pendulum equation). In the natural sciences, the term "vector quantity" also encompasses vector fields defined over a two-or three-dimensional region of space, such as wind velocity over Earth's surface.
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. [9] [10] It is typically formulated as the product of a unit of measurement and a vector numerical value (), often a Euclidean vector with magnitude and direction.
Momentum is a vector quantity, so impulse is also a vector quantity. Newton’s second law of motion states that the rate of change of momentum of an object is equal to the resultant force F acting on the object: =,
Similarly, the momentum is a vector quantity and is represented by a boldface symbol: = (,,). The equations in the previous sections, work in vector form if the scalars p and v are replaced by vectors p and v. Each vector equation represents three scalar equations. For example,
To calculate the flux of a vector field F (red arrows) through a surface S the surface is divided into small patches dS. The flux through each patch is equal to the normal (perpendicular) component of the field, the dot product of F ( x ) with the unit normal vector n ( x ) (blue arrows) at the point x multiplied by the area dS .
It is a vector quantity (having both magnitude and direction). Jerk is most commonly denoted by the symbol j and expressed in m/s 3 ( SI units ) or standard gravities per second ( g 0 /s). Expressions
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.
Mathematically, mass flux is defined as the limit =, where = = is the mass current (flow of mass m per unit time t) and A is the area through which the mass flows.. For mass flux as a vector j m, the surface integral of it over a surface S, followed by an integral over the time duration t 1 to t 2, gives the total amount of mass flowing through the surface in that time (t 2 − t 1): = ^.