At conference and through home work problems you have been introduced to the idea of a vector. In short vectors allow us to represent a magnitude as well as a direction in a single mathematical object. It is important that a vector alone does not specify a location in space, just a displacement. So when you draw a vector you are always free to choose its location in space. Only in conjunction with a specific origin can a vector specify a location and then we call it a position vector.
Two vectors can be combined in
various ways to form a resulting vector. Until now you have seen
vector addition and subtraction. In short for addition put vectors head
to tail and the resulting vector goes from
tail to head. For subtraction (
)
put vectors head to head and
remember that the resulting vector points from the tail of 
to the tail
of 
. Note that even though vector subtraction and addition
formally are very similar to addition and subtraction of scalars the
geometrical content is unique to vector addition.