Vectors are representations of directed line segments.

Each of them has a length given by the length of the corresponding segment, as well as a direction.

We can add them, forming a + b by starting b at the end of a; the sum is then the third side of the triangle they form.

We can change their length by an arbitrary numerical factor by multiplying the vector by that factor. If the factor is negative the direction of the segment is reversed.

If we take two vectors, a and b, they define an angle between them, and they each have lengths.