1
Vectors – what are they?

Vectors describe
movements

i, j and k represent
movement in the x,y
and z directions
Maths revision course by Miriam Hanks
2
Vectors – How to calculate
A
B
To calculate vector BA,
subtract:
BA = a - b
O
Maths revision course by Miriam Hanks
3
Vectors - resultants
To find the resultant, add the components of
the vectors together
resultant
Maths revision course by Miriam Hanks
4
Vectors - magnitude
The magnitude of a vector is its length.
The notation for this is vertical lines:
eg |a| or |PQ|
To find the magnitude of a vector, use
Pythagoras or the distance formula.
Maths revision course by Miriam Hanks
5
Vectors - Collinearity
To show that 3 points are in a
straight line (ie collinear):

Work out 2 vectors and
show that one is a multiple
of the other

Show that the vectors have
a common point
Maths revision course by Miriam Hanks
6
Vectors in real life
Sat navs work out
their position from
satellites in the sky,
but then use vectors
to decide on a route.
Maths revision course by Miriam Hanks
7
Vectors – Dot product
There are 2 formulae for the dot product on the
formula sheet:

dot product = x1x2 + y1 y2 +z1z2
where x,y,z are the components of each vector.

dot product = a bcos
where a is the magnitude of vector a (use Pythagoras for this)
Note these 2 formulae equal each other, so:
a bcos = x1x2 + y1 y2 +z1z2
Maths revision course by Miriam Hanks
8
Dot product of vectors at 90
o
o
The dot product of 2 vectors at 90 is
zero
and vice versa
Why?
Maths revision course by Miriam Hanks
9
Dot product of a vector with itself
The dot product of vector a with itself is:
a2
Why?
Maths revision course by Miriam Hanks
10
The dot product in real life
When is the dot product used in real life?
Computer games programmers use the dot product to
find the angle between 2 characters, so they know
whether they are facing each other.
Maths revision course by Miriam Hanks