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Coincident
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Coincident is a geometric term that pertains to the relationship between two vectors. Vectors consist of a "magnitude" and a "direction". Vectors can be said to be coincident when their direction is the same though the magnitude may be different; that is to say, they lie one on top of the other. If two coincident vectors were to be normalized (shortened or lengthened to be one unit long), the resulting vectors would be identical. The dot product of two coincident vectors is the product of their magnitudes. The cross product of two coincident vectors is a vector of all zeros.
Coincidence
From Wikipedia, the free encyclopedia
A coincidence is the occurring of an event in conjunction with any some conditions, e.g. another event. As such, a coincidence occurs when something uncanny, accidental and unexpected happens under conditions named, but not under a defined relationship. When there are no conditions named, the event is just that single entity.
The word is derived from the Latin co- ("in", "with", "together") and incidere ("to fall on"). In science, the term is generally used in a more literal translation, e.g., referring to when two rays of light strike a surface at the same point at the same time. In this usage of coincidence, there is no implication that the alignment of events is surprising, noteworthy or non-causal.
A coincidence does not prove a causal or any other modal relationship nor require any such. In the field of mathematics, the index of coincidence can be used to analyze whether two events are related. Such index does not define any relationship, but just describes some possibility of such. Physically related events may be expected to have a higher probability to occur, probability is the basic metrics, or method, to rationally evaluate physical coincidences.