Vectors
Vectors are values that have a size
and direction
They can be represented as...
Lower case letters that are underlined
(or bold) represent vectors
Vectors can also be written as going from
one point to another such as .
Addition and subtraction of vectors
 refer to the blue vectors
+
=
+
= +
=
in additions, you can swap the order of the vectors

= +
=
swapping the order of the letters within a vector makes positive vectors
negative (because forwards from B to C is backwards from C to B!)
Proof
You can provide proof for something by
finding that...
 two vectors are the same
(therefore they are parallel and the same length)
 two vectors are multiples of each other
(therefore parallel but different lengths)
e.g. Prove that PQRS is a parallelogram
(P, Q, R and S are all midpoints of the lines they are on)
In order to do this, we need to show
that two sides have the same size and direction...
=
+
= ½
+ ½
= ½ (
+ )
*
= ½ *
=
+
= ½
+ ½
= ½ (
+ )
*
= ½ *
Therefore
= so PQRS is a parallelogram