VECTOR ADDITION
Introduction
to Vector Addition and Scalar Multiplication
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.
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