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In physics, a plane wave is a special case of a wave or field: a physical quantity whose value, at any moment, is constant through any plane that is perpendicular to a fixed direction in space. [1] For any position in space and any time , the value of such a field can be written as (,) = (,), where is a unit-length vector, and (,) is a function ...
By definition, all Euclidean vectors have a magnitude (see above). However, a vector in an abstract vector space does not possess a magnitude. A vector space endowed with a norm, such as the Euclidean space, is called a normed vector space. [8] The norm of a vector v in a normed vector space can be considered to be the magnitude of v.
This plane lies at distance from the origin when =, and travels in the direction ^ also with speed ; and the value of the field is then the same, and constant in time, at every one of its points. A sinusoidal plane wave could be a suitable model for a sound wave within a volume of air that is small compared to the distance of the source ...
A vector field for the movement of air on Earth will associate for every point on the surface of the Earth a vector with the wind speed and direction for that point. This can be drawn using arrows to represent the wind; the length ( magnitude ) of the arrow will be an indication of the wind speed.
Newton's law of gravitation resembles Coulomb's law of electrical forces, which is used to calculate the magnitude of the electrical force arising between two charged bodies. Both are inverse-square laws, where force is inversely proportional to the square of the distance between the bodies. Coulomb's law has charge in place of mass and a ...
In three-dimensional space, we again have the position vector r of a moving particle. Here, orbital angular velocity is a pseudovector whose magnitude is the rate at which r sweeps out angle (in radians per unit of time), and whose direction is perpendicular to the instantaneous plane in which r sweeps out angle (i.e. the plane spanned by r and v).
Speed, the scalar magnitude of a velocity vector, denotes only how fast an object is moving, while velocity indicates both an object's speed and direction. [3] [4] [5] To have a constant velocity, an object must have a constant speed in a constant direction. Constant direction constrains the object to motion in a straight path thus, a constant ...
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. [1] It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory.