Multiplying Vectors by a Scalar
Vectors can be multiplied by a
scalar which changes the size of the vector but not the direction.

The vector 2k is twice as long as the vector k. Double each number in to get 2k.



The vector 1/2 m is half as long as the vector m. Halve each number in m to get 1/2 m.


Adding Vectors
Vectors can be added by drawing the first vector, then starting the second vector where the first vector ends.


The single vector they create

is the
resultant vector.
Travelling from X to Y, then from Y to Z, is the same as travelling from X to Z.
Subtracting Vectors
Subtracting a vector is the same as adding a negative vector.


Since the vector

has the same magnitude but opposite direction to the vector


Example: Write, in terms of a and b, the vector 

