1. Vectors
Definition:
A vector quantity is one which has both magnitude and direction
One of the simplest vectors is called a displacement… it has an associated distance (magnitude) and direction.
For example, if we have two points A and B then ‘displacement AB’ is a vector quantity.
It can be conveniently represented by a straight line joining A and B, and the direction indicated by an arrow. A B

2. The length of the line AB represents the distance between A and B
The length of the line AB represents the distance between A and B. For ‘vector AB’ we write either AB or
and textbooks use bold type.
Another notation involves the use of lower case letters
‘vector r’ r

3. Definition:
A scalar quantity is one which has magnitude only.
In the context of the previous example ‘distance travelled’ is a scalar quantity.
A displacement vector in two dimensions is conveniently expressed in component form, as a column vector. a b c d

4. a + b a – b Addition and Subtraction using components
We can see displacement a followed by displacement b which is… c b
entirely equivalent to the single displacement c.
We write c = a + b a
a + b
a – b

5. Multiplication of a vector by a scalar
Consider the vectors a, 3a, -a, -2a a 3a -a
-2a
They are parallel vectors
Parallel vectors
If a and b are parallel then for some scalar quantity, , it must follow that a = b
If a = b then a and b are parallel

6. Modulus of a vector: is its magnitude and hence a scalar.
The modulus of a is written |a| and is written usually as a.
Magnitude of a vector in component form
Example a
In general