Explanation:
Euclidean vector
Illustration
of a vector
A
vector going from A to B
In elementary mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or - as here - simply a
vector) is a geometric object that has both a magnitude (or length) and direction. A
Euclidean vector is frequently represented by a line segment with a definite direction, or
graphically as an arrow, connecting an initial point A with a terminal point B, and denoted by
http://en.wikipedia.org/wiki/Euclidean_vector
In mathematics, the dot product is an algebraic operation that
takes two equal-length sequences of numbers (usually coordinate vectors) and returns
a single number obtained by multiplying corresponding entries and then summing
those products. The name is derived from the centered dot "·" that is often used to
designate this operation; the alternative name scalar product emphasizes the scalar (rather than vector) nature of the result.
At a basic level, the dot product is used to obtain the cosine of the angle
between two vectors.
Geometric
interpretation
is the scalar projection of onto .
Since, then .
In Euclidean geometry, the dot
product of vectors expressed in an orthonormal basis is related to their length and angle. For such a vector , the dot product is the square of the length
of , or
where denotes the length (magnitude) of . If is another such vector,
where θ is the angle between them.
This formula
can be rearranged to determine the size of the angle between two nonzero
vectors:
(Our solved example in mathguru.com uses
this concept)
http://en.wikipedia.org/wiki/Dot_product
The above explanation is copied from
Wikipedia, the free encyclopedia and is remixed as allowed under the Creative Commons
Attribution- ShareAlike 3.0 Unported License.