1. Maths revision course by Miriam Hanks
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. Maths revision course by Miriam Hanks
Vectors – How to calculate
To calculate vector BA,
subtract:
BA = a - b A B O
Maths revision course by Miriam Hanks

3. Maths revision course by Miriam Hanks
Vectors - resultants
To find the resultant, add the components of the vectors together
resultant
Maths revision course by Miriam Hanks

4. Maths revision course by Miriam Hanks
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. Maths revision course by Miriam Hanks
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. Maths revision course by Miriam Hanks
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. Maths revision course by Miriam Hanks
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. Maths revision course by Miriam Hanks
Dot product of vectors at 90o
The dot product of 2 vectors at 90o is
zero
and vice versa
Why?
Maths revision course by Miriam Hanks

9. Maths revision course by Miriam Hanks
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. Maths revision course by Miriam Hanks
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