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In mathematics, a unit vector in a normed vector space is a vector (often a spatial vector) of length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in ^ (pronounced "v-hat"). The term normalized vector is sometimes used as a synonym for unit vector. The normalized vector û of a non-zero vector u is the ...
In mathematics and physics, vector notation is a commonly used notation for representing vectors, [1] [2] which may be Euclidean vectors, or more generally, members of a vector space. For denoting a vector, the common typographic convention is lower case, upright boldface type, as in v .
This angle may be calculated from the dot product of the two vectors, defined as a ⋅ b = ‖ a ‖ ‖ b ‖ cos θ where ‖ a ‖ denotes the length of vector a. As shown in the diagram, the dot product here is –1 and the length of each vector is √ 3 , so that cos θ = – 1 / 3 and the tetrahedral bond angle θ = arccos ...
Accropode (1981) The Accropode is a single-layer artificial armour unit developed by Sogreah in 1981. Accropode concrete armour units are applied in a single layer. Ecopode (1996) The Ecopode armour unit with a rock-like appearance was developed by Sogreah to enhance the natural appearance of concrete armourings above low water level.
This definition can be formalized in Cartesian space by defining the dot product and specifying that two vectors in the plane are orthogonal if their dot product is zero. Similarly, the construction of the norm of a vector is motivated by a desire to extend the intuitive notion of the length of a vector to higher-dimensional spaces.
A free vector is a vector quantity having an undefined support or region of application; it can be freely translated with no consequences; a displacement vector is a prototypical example of free vector. Aside from the notion of units and support, physical vector quantities may also differ from Euclidean vectors in terms of metric.
A primitive cell is a unit cell that contains exactly one lattice point. For unit cells generally, lattice points that are shared by n cells are counted as 1 / n of the lattice points contained in each of those cells; so for example a primitive unit cell in three dimensions which has lattice points only at its eight vertices is considered to contain 1 / 8 of each of them. [3]
An example of the tetragonal crystals, wulfenite Two different views (top down and from the side) of the unit cell of tP30-CrFe (σ-phase Frank–Kasper structure) that show its different side lengths, making this structure a member of the tetragonal crystal system. In crystallography, the tetragonal crystal system is one of the 7 crystal systems.