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A four-vector A is a vector with a "timelike" component and three "spacelike" components, and can be written in various equivalent notations: [3] = (,,,) = + + + = + = where A α is the magnitude component and E α is the basis vector component; note that both are necessary to make a vector, and that when A α is seen alone, it refers strictly to the components of the vector.
The vector of coordinates forms the coordinate vector or n-tuple (x 1, x 2, …, x n). Each coordinate x i may be parameterized a number of parameters t. One parameter x i (t) would describe a curved 1D path, two parameters x i (t 1, t 2) describes a curved 2D surface, three x i (t 1, t 2, t 3) describes a curved 3D volume of space, and so on.
A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier". [4] It was first used by 18th century astronomers investigating planetary revolution around the Sun. [5] The magnitude of the vector is the distance between the two points, and the direction refers to the direction of displacement from A to B.
In linear algebra, a column vector with elements is an matrix [1] consisting of a single column of entries, for example, = [].. Similarly, a row vector is a matrix for some , consisting of a single row of entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)
[2] [3] Therefore, the magnitude of the four-acceleration (which is an invariant scalar) is equal to the proper acceleration that a moving particle "feels" moving along a worldline. A worldline having constant four-acceleration is a Minkowski-circle i.e. hyperbola (see hyperbolic motion )
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.
This set of models is often referred to collectively as SGP4 due to the frequency of use of that model particularly with two-line element sets produced by NORAD and NASA. These models predict the effect of perturbations caused by the Earth’s shape, drag, radiation, and gravitation effects from other bodies such as the sun and moon.
In terms of model railway operation, gauge 3 is the largest (standard gauge) scenic railway modelling scale, using a scale of 13.5 mm to the foot. The Gauge '3' Society represents this aspect of 2 + 1 ⁄ 2-inch gauge railway modelling with both electric and live steam operation. Gauge '3' corresponds to NEM II scale, also known as "Spur II" in ...