A vector is a quantity with **dimensions, a magnitude, and
a direction** relative to a **specific coordinate frame**. Note
that it isn't sufficient to have a list of (say) three numbers labelled
,
, and
- the components have to transform when the
underlying coordinate frame is transformed ``like a vector''. Although
there are multiple coordinate systems in which vectors can be expressed,
the ``simplest'' one is Cartesian, where a vector can typically be
written:

in terms of component scalar amplitudes and unit vectors in the orthogonal directions .

To add vectors (in Cartesian coordinates) we add components:

The resultant is also the result of a geometric triangle or parallelogram rule:

vector-sum.eps

Subtraction is just addition of a negative:

It can also be visualized by means of a geometric triangle so that .

vector-difference.eps

- Scalars and Vectors
- The Scalar, or Dot Product

- The Vector, or Cross Product
- Triple Products of Vectors
- &delta#delta;_ij and &epsi#epsilon;_ijk