a= ( 3, 2 )^{T}b= (-2, 1 )^{T}

a + b= ( 1, 3 )^{T}

Vectors are geometric objects. A particular vector can be represented in a variety of ways. It is important to understand the difference between a geometric object (such as a point or a vector) and the way it is represented (often with a column matrix).

The diagram shows points A, B, and C (in two dimensions).
A displacement is a distance and a direction.
Vector **u** is the displacement from A to B.
Vector **v** is the displacement from B to C.

The displacement from A to C is the vector **w**.
The effect of moving through the displacement **u** and then
through the displacement **v** is the same as moving through
the displacement **w**.
In symbols:

u+v=w