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This glossary of physics is a list of definitions of terms and concepts relevant to physics, its sub-disciplines, and related fields, including mechanics, materials science, nuclear physics, particle physics, and thermodynamics.
In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space.
Since ε 2 = 0 for dual numbers, exp(aε) = 1 + aε, all other terms of the exponential series vanishing. Let F = {1 + εr : r ∈ H}, ε 2 = 0. Note that F is stable under the rotation q → p −1 qp and under the translation (1 + εr)(1 + εs) = 1 + ε(r + s) for any vector quaternions r and s. F is a 3-flat in the eight-dimensional space of ...
Ordered pairs of scalars are sometimes called 2-dimensional vectors. (Technically, this is an abuse of terminology since an ordered pair need not be an element of a vector space.) The entries of an ordered pair can be other ordered pairs, enabling the recursive definition of ordered n-tuples (ordered lists of n objects).
A vector pointing from A to B. In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector [1] or spatial vector [2]) is a geometric object that has magnitude (or length) and direction. Euclidean vectors can be added and scaled to form a vector space.
In other words, a couple, unlike any more general moments, is a "free vector". (This fact is called Varignon's Second Moment Theorem.) [2] The proof of this claim is as follows: Suppose there are a set of force vectors F 1, F 2, etc. that form a couple, with position vectors (about some origin P), r 1, r 2, etc., respectively.
Figure 1: Parallelogram construction for adding vectors. This construction has the same result as moving F 2 so its tail coincides with the head of F 1, and taking the net force as the vector joining the tail of F 1 to the head of F 2. This procedure can be repeated to add F 3 to the resultant F 1 + F 2, and so forth.
Given a vector at the north pole, one can transport this vector along a curve by rotating the sphere in such a way that the north pole moves along the curve without axial rolling. This latter means of parallel transport is the Levi-Civita connection on the sphere.