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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.
The notations (î, ĵ, k̂), (x̂ 1, x̂ 2, x̂ 3), (ê x, ê y, ê z), or (ê 1, ê 2, ê 3), with or without hat, are also used, [1] particularly in contexts where i, j, k might lead to confusion with another quantity (for instance with index symbols such as i, j, k, which are used to identify an element of a set or array or sequence of ...
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.
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.
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.)
The scalar projection is defined as [2] = ‖ ‖ = ^ where the operator ⋅ denotes a dot product, ‖a‖ is the length of a, and θ is the angle between a and b. The scalar projection is equal in absolute value to the length of the vector projection, with a minus sign if the direction of the projection is opposite to the direction of b ...
While HO scale is a 1:87 scale (3.5 mm to 1 foot), resulting in a 16.5 mm (0.65 in) gauge from real life prototype 1,435 mm (4 ft 8 + 1 ⁄ 2 in) standard gauge standard gauge. Conversely, modeling standard gauge in Lego trains would yield a scaling of (37.5:1435 =) 1:38.3.
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.