A vector is a magnitude with a direction. Much of physics deals with vectors. An -dimensional vector can be thought of as an ordered -tuple of numbers within angle brackets. The set of vectors in some space is an example of a vector space.
Every vector has a starting point and an endpoint . Since the only thing that distinguishes one vector from another is its magnitude,i.e. length, and direction, vectors can be freely translated about a plane without changing them. Hence, it is convenient to consider a vector as originating from the origin. This way, two vectors can be compared only by looking at their endpoints. The magnitude of a vector, denoted is found simply by using the distance formula.
Properties of Vectors
Dot (Scalar) Product (proof as well? ) (--use law of cosines; I'm not good at proofs--from Aryth)
Consider two vectors and . The dot product is defined as . In two or three dimensions, the dot product has the special geometric property that
Cross (Vector) Product
Triple Scalar product
Triple Vector Product
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