In the strictly mathematical definition of a vector, the only operations
that vectors are required to possess are those of addition and scalar
multiplication. (Compare this with the operations allowed on ordinary real
numbers, or scalars, in which we are given addition, subtraction,
multiplication, and division). For instance, in a raw vector space there is no
obvious way to multiply two vectors together to get a third vector--even though
we *will* define a couple of ways of performing vector multiplication in
Vector Multiplication.

It makes sense, then, to begin studying vectors with an investigation of the operations of vector addition and scalar multiplication. This section will be entirely devoted to explaining addition and scalar multiplication of two- and three-dimensional vectors. This explanation will involve two different, yet equivalent, methods: the component method and the graphical method.