12.2 Vectors
Scalars are quantities that only have a magnitude like mass, speed, and electric field strength. Many
times it is often useful to have a quantity that has not only a magnitude but also a direction; such a
quantity is called a
vector
. Examples of quantities represented by vectors include velocity,
acceleration, and virtually any type of force (frictional, gravitational, electric, magnetic, etc.). Note
that all of these quantities not only have a magnitude (such as speed – the magnitude of the velocity
vector) but also occur or act in a given direction.
It is convenient to represent both quantities by just one symbol, the vector. Graphically, a vector is
represented by an arrow, defining the direction, and the length of the arrow defining the vector's
magnitude.
A
twodimensional
vector
is an ordered pair
1
2
,
a
a
=
a
of real numbers.
A
threedimensional vector
is an ordered triple
1
2
3
,
,
a
a
a
=
a
of real numbers.
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 Fall '08
 Estrada
 Linear Algebra, Vectors, Scalar, Vector Space, Standard basis

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