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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...

= +

= +

= ( + )

* = *

 

= +

= +

= ( + )

* = *

 

Therefore = so PQRS is a parallelogram

 

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