Introduction to Vectors (Cambridge (CIE) IGCSE International Maths)
Revision Note
Basic Vectors
What is a vector?
Vectors represent a movement of a certain distance (magnitude) in a given direction
In one dimension, the sign of a number represents its direction
For example, two objects with velocities 7 m/s and ‑7 m/s are travelling:
at the same speed (magnitude)
but in opposite directions
In two dimensions, vectors consist of x- and y-components
These show movement parallel to the x- and y-axes
Components can be positive or negative
How do I write vectors?
You can write the two components of a vector as a column vector
E.g. is 3 right and 2 up
A lower-case letter can be used to represent the vector if the two components are not known
Exams use bold letters
a, b, ...
You should write underlined letters
a, b, ...
Vectors can also be described by their start and end points
If points (A , B , ...) are given
means the vector from A to B
The order of the letters matters
How are vectors used on a grid?
Vectors are often drawn on a grid (with or without x- and y-axes)
They can also be represented using column vectors
How do I multiply a vector by a scalar?
A scalar is a number with a magnitude but no direction
When a vector is multiplied by a positive scalar:
the magnitude of the vector changes
its direction stays the same
For a vector represented as a column vector
each of the numbers in the column vector will be multiplied by the scalar
When a vector is multiplied by a negative scalar:
the magnitude of the vector changes
its direction reverses
How do I add vectors?
To add vectors you add their components
For column vectors, add the tops together and bottoms together
Visually, the vector a + b is the shortest route
from the start of a
to the end of b
How do I subtract vectors?
To subtract vectors you subtract their components
Subtracting a vector can also be thought of as adding a negative vector
Visually, the vector a - b is the shortest route
from the start of a
to the end of -b
Worked Example
The points A, B and C are shown on the following coordinate grid.
a) Write the vectors and as column vectors.
Start by drawing the three vectors onto the grid
From A to B, it is 6 to the right and 2 up
From A to C, it is 7 to the right and 6 down
From C to B, it is 1 to the left and 8 up
b) Using the column vectors from a), confirm that .
Perform the subtraction on the column vectors
c) Write as a column vector.
Multiply all parts of the vector by
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