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An antenna mast with four collinear directional arrays. In telecommunications, a collinear (or co-linear) antenna array is an array of dipole antennas mounted in such a manner that the corresponding elements of each antenna are parallel and aligned, that is they are located along a common line or axis.
In three-dimensional space, two linearly independent vectors with the same initial point determine a plane through that point. Their cross product is a normal vector to that plane, and any vector orthogonal to this cross product through the initial point will lie in the plane. [ 1 ]
Tangential – intersecting a curve at a point and parallel to the curve at that point. Collinear – in the same line; Parallel – in the same direction. Transverse – intersecting at any angle, i.e. not parallel. Orthogonal (or perpendicular) – at a right angle (at the point of intersection).
Consider n-dimensional vectors that are formed as a list of n scalars, such as the three-dimensional vectors = [] = []. These vectors are said to be scalar multiples of each other, or parallel or collinear , if there is a scalar λ such that x = λ y . {\displaystyle \mathbf {x} =\lambda \mathbf {y} .}
There exist four points such that no three are collinear (points not on a single line). In an affine plane, two lines are called parallel if they are equal or disjoint. Using this definition, Playfair's axiom above can be replaced by: [2] Given a point and a line, there is a unique line which contains the point and is parallel to the line.
In physics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly opposite to the corresponding vectors.
Line segments and Euclidean vectors are parallel if they have the same direction or opposite direction (not necessarily the same length). [1] Parallel lines are the subject of Euclid's parallel postulate. [2] Parallelism is primarily a property of affine geometries and Euclidean geometry is a special instance of this type of geometry.
However, parallel (non-crossing) pairs of lines are less restricted in hyperbolic line arrangements than in the Euclidean plane: in particular, the relation of being parallel is an equivalence relation for Euclidean lines but not for hyperbolic lines. [51] The intersection graph of the lines in a hyperbolic arrangement can be an arbitrary ...